Does it really make sense to talk about the color of gluons?












4














It is my understanding that by enforcing SU(3) gauge invariance on our lagrangian of 3-colored quark fields, we are forced to accept the existence of 8 new massless vector fields, the gluons. The 8 here comes directly from the dimension of SU(3).



That being said I often see discussions about the gluons in terms of linear combinations of $rbar r$, $bbar b$, etc.



This simply cant be the nature of the gluons though can it? Because it seems to imply that the number of colors and the number of gluon fuelds are not independant, while they clearly are.



Certainly gluons are not singlets in color space and so they must have color, but it doesnt make sense to me that this color of the gluons would be some mapping directly from quark color.



Thanks to anyone with the insight and time to share it!






quantum-chromodynamics gauge-invariance strong-force







share|cite|improve this question





























    4














    It is my understanding that by enforcing SU(3) gauge invariance on our lagrangian of 3-colored quark fields, we are forced to accept the existence of 8 new massless vector fields, the gluons. The 8 here comes directly from the dimension of SU(3).



    That being said I often see discussions about the gluons in terms of linear combinations of $rbar r$, $bbar b$, etc.



    This simply cant be the nature of the gluons though can it? Because it seems to imply that the number of colors and the number of gluon fuelds are not independant, while they clearly are.



    Certainly gluons are not singlets in color space and so they must have color, but it doesnt make sense to me that this color of the gluons would be some mapping directly from quark color.



    Thanks to anyone with the insight and time to share it!






    quantum-chromodynamics gauge-invariance strong-force







    share|cite|improve this question



























      4












      4








      4


      1





      It is my understanding that by enforcing SU(3) gauge invariance on our lagrangian of 3-colored quark fields, we are forced to accept the existence of 8 new massless vector fields, the gluons. The 8 here comes directly from the dimension of SU(3).



      That being said I often see discussions about the gluons in terms of linear combinations of $rbar r$, $bbar b$, etc.



      This simply cant be the nature of the gluons though can it? Because it seems to imply that the number of colors and the number of gluon fuelds are not independant, while they clearly are.



      Certainly gluons are not singlets in color space and so they must have color, but it doesnt make sense to me that this color of the gluons would be some mapping directly from quark color.



      Thanks to anyone with the insight and time to share it!






      quantum-chromodynamics gauge-invariance strong-force







      share|cite|improve this question















      It is my understanding that by enforcing SU(3) gauge invariance on our lagrangian of 3-colored quark fields, we are forced to accept the existence of 8 new massless vector fields, the gluons. The 8 here comes directly from the dimension of SU(3).



      That being said I often see discussions about the gluons in terms of linear combinations of $rbar r$, $bbar b$, etc.



      This simply cant be the nature of the gluons though can it? Because it seems to imply that the number of colors and the number of gluon fuelds are not independant, while they clearly are.



      Certainly gluons are not singlets in color space and so they must have color, but it doesnt make sense to me that this color of the gluons would be some mapping directly from quark color.



      Thanks to anyone with the insight and time to share it!






      quantum-chromodynamics gauge-invariance strong-force




      quantum-chromodynamics gauge-invariance strong-force






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Nov 10 at 18:55

























      asked Nov 10 at 18:03









      Craig

      1119




      1119






















          1 Answer
          1






          active

          oldest

          votes


















          6














          The quarks transform according to the fundamental representation $mathbf{3}$ of SU(3), and the antiquarks according to the conjugate representation $mathbf{overline 3}$. The gluons transform according to the adjoint representation $mathbf{8}$.



          The adjoint representation is contained in the product of the fundamental representation and its conjugate:



          $$mathbf{3}otimes mathbf{overline 3} = mathbf{8}oplus mathbf{1}$$



          Therefore gluons are conventionally labeled using color-anticolor combinations, avoiding the color singlet combination $(roverline{r}+boverline{b}+goverline{g})/sqrt{3}$.






          share|cite|improve this answer























          • Awesome do you have a any sources/papers/books I could find more about this?
            – Craig
            Nov 10 at 18:53










          • As well; in a universe where we had say, 4 or 5 colors and 8 gluons, how would this work?
            – Craig
            Nov 10 at 18:57






          • 1




            @Craig, are you familiar with representation theory? A big concept is that the same group can be "represented" with larger or smaller vector spaces. In this case, the quarks have the minimum number of vectors needed to realize SU(3) symmetry, and the gluons have (very loosely) that maximum number of vectors that can have the SU(3) symmetry, one for each dimension. If we had 4 colors, then we would instead want $4otimes bar 4 = 15oplus 1$, and we would have 15 gluon fields for the 4 colors.
            – Alex Meiburg
            Nov 10 at 19:01










          • The adjoint reprsentation of SU(n) has dimension $n^2-1$. So if you have 4 colors there need to be 15 gluons and if you have 5 colors there need to be 24 gluons.
            – G. Smith
            Nov 10 at 19:05










          • I’ll let others suggest the best references. But you need to clarify what you main interest is. The mathematics of representation theory? (For example, how do you figure out how an arbitrary product of irreducible representations decomposes into irreducible representations?) The physics of QCD, or the whole Standard Model? The reason why quantum field theory involves group representations? Etc.
            – G. Smith
            Nov 10 at 20:25













          Your Answer





          StackExchange.ifUsing("editor", function () {
          return StackExchange.using("mathjaxEditing", function () {
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          });
          });
          }, "mathjax-editing");

          StackExchange.ready(function() {
          var channelOptions = {
          tags: "".split(" "),
          id: "151"
          };
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function() {
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled) {
          StackExchange.using("snippets", function() {
          createEditor();
          });
          }
          else {
          createEditor();
          }
          });

          function createEditor() {
          StackExchange.prepareEditor({
          heartbeatType: 'answer',
          autoActivateHeartbeat: false,
          convertImagesToLinks: false,
          noModals: true,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: null,
          bindNavPrevention: true,
          postfix: "",
          imageUploader: {
          brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
          contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
          allowUrls: true
          },
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          });


          }
          });














          draft saved

          draft discarded


















          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f440142%2fdoes-it-really-make-sense-to-talk-about-the-color-of-gluons%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown

























          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          6














          The quarks transform according to the fundamental representation $mathbf{3}$ of SU(3), and the antiquarks according to the conjugate representation $mathbf{overline 3}$. The gluons transform according to the adjoint representation $mathbf{8}$.



          The adjoint representation is contained in the product of the fundamental representation and its conjugate:



          $$mathbf{3}otimes mathbf{overline 3} = mathbf{8}oplus mathbf{1}$$



          Therefore gluons are conventionally labeled using color-anticolor combinations, avoiding the color singlet combination $(roverline{r}+boverline{b}+goverline{g})/sqrt{3}$.






          share|cite|improve this answer























          • Awesome do you have a any sources/papers/books I could find more about this?
            – Craig
            Nov 10 at 18:53










          • As well; in a universe where we had say, 4 or 5 colors and 8 gluons, how would this work?
            – Craig
            Nov 10 at 18:57






          • 1




            @Craig, are you familiar with representation theory? A big concept is that the same group can be "represented" with larger or smaller vector spaces. In this case, the quarks have the minimum number of vectors needed to realize SU(3) symmetry, and the gluons have (very loosely) that maximum number of vectors that can have the SU(3) symmetry, one for each dimension. If we had 4 colors, then we would instead want $4otimes bar 4 = 15oplus 1$, and we would have 15 gluon fields for the 4 colors.
            – Alex Meiburg
            Nov 10 at 19:01










          • The adjoint reprsentation of SU(n) has dimension $n^2-1$. So if you have 4 colors there need to be 15 gluons and if you have 5 colors there need to be 24 gluons.
            – G. Smith
            Nov 10 at 19:05










          • I’ll let others suggest the best references. But you need to clarify what you main interest is. The mathematics of representation theory? (For example, how do you figure out how an arbitrary product of irreducible representations decomposes into irreducible representations?) The physics of QCD, or the whole Standard Model? The reason why quantum field theory involves group representations? Etc.
            – G. Smith
            Nov 10 at 20:25


















          6














          The quarks transform according to the fundamental representation $mathbf{3}$ of SU(3), and the antiquarks according to the conjugate representation $mathbf{overline 3}$. The gluons transform according to the adjoint representation $mathbf{8}$.



          The adjoint representation is contained in the product of the fundamental representation and its conjugate:



          $$mathbf{3}otimes mathbf{overline 3} = mathbf{8}oplus mathbf{1}$$



          Therefore gluons are conventionally labeled using color-anticolor combinations, avoiding the color singlet combination $(roverline{r}+boverline{b}+goverline{g})/sqrt{3}$.






          share|cite|improve this answer























          • Awesome do you have a any sources/papers/books I could find more about this?
            – Craig
            Nov 10 at 18:53










          • As well; in a universe where we had say, 4 or 5 colors and 8 gluons, how would this work?
            – Craig
            Nov 10 at 18:57






          • 1




            @Craig, are you familiar with representation theory? A big concept is that the same group can be "represented" with larger or smaller vector spaces. In this case, the quarks have the minimum number of vectors needed to realize SU(3) symmetry, and the gluons have (very loosely) that maximum number of vectors that can have the SU(3) symmetry, one for each dimension. If we had 4 colors, then we would instead want $4otimes bar 4 = 15oplus 1$, and we would have 15 gluon fields for the 4 colors.
            – Alex Meiburg
            Nov 10 at 19:01










          • The adjoint reprsentation of SU(n) has dimension $n^2-1$. So if you have 4 colors there need to be 15 gluons and if you have 5 colors there need to be 24 gluons.
            – G. Smith
            Nov 10 at 19:05










          • I’ll let others suggest the best references. But you need to clarify what you main interest is. The mathematics of representation theory? (For example, how do you figure out how an arbitrary product of irreducible representations decomposes into irreducible representations?) The physics of QCD, or the whole Standard Model? The reason why quantum field theory involves group representations? Etc.
            – G. Smith
            Nov 10 at 20:25
















          6












          6








          6






          The quarks transform according to the fundamental representation $mathbf{3}$ of SU(3), and the antiquarks according to the conjugate representation $mathbf{overline 3}$. The gluons transform according to the adjoint representation $mathbf{8}$.



          The adjoint representation is contained in the product of the fundamental representation and its conjugate:



          $$mathbf{3}otimes mathbf{overline 3} = mathbf{8}oplus mathbf{1}$$



          Therefore gluons are conventionally labeled using color-anticolor combinations, avoiding the color singlet combination $(roverline{r}+boverline{b}+goverline{g})/sqrt{3}$.






          share|cite|improve this answer














          The quarks transform according to the fundamental representation $mathbf{3}$ of SU(3), and the antiquarks according to the conjugate representation $mathbf{overline 3}$. The gluons transform according to the adjoint representation $mathbf{8}$.



          The adjoint representation is contained in the product of the fundamental representation and its conjugate:



          $$mathbf{3}otimes mathbf{overline 3} = mathbf{8}oplus mathbf{1}$$



          Therefore gluons are conventionally labeled using color-anticolor combinations, avoiding the color singlet combination $(roverline{r}+boverline{b}+goverline{g})/sqrt{3}$.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited Nov 11 at 20:17

























          answered Nov 10 at 18:49









          G. Smith

          3,933918




          3,933918












          • Awesome do you have a any sources/papers/books I could find more about this?
            – Craig
            Nov 10 at 18:53










          • As well; in a universe where we had say, 4 or 5 colors and 8 gluons, how would this work?
            – Craig
            Nov 10 at 18:57






          • 1




            @Craig, are you familiar with representation theory? A big concept is that the same group can be "represented" with larger or smaller vector spaces. In this case, the quarks have the minimum number of vectors needed to realize SU(3) symmetry, and the gluons have (very loosely) that maximum number of vectors that can have the SU(3) symmetry, one for each dimension. If we had 4 colors, then we would instead want $4otimes bar 4 = 15oplus 1$, and we would have 15 gluon fields for the 4 colors.
            – Alex Meiburg
            Nov 10 at 19:01










          • The adjoint reprsentation of SU(n) has dimension $n^2-1$. So if you have 4 colors there need to be 15 gluons and if you have 5 colors there need to be 24 gluons.
            – G. Smith
            Nov 10 at 19:05










          • I’ll let others suggest the best references. But you need to clarify what you main interest is. The mathematics of representation theory? (For example, how do you figure out how an arbitrary product of irreducible representations decomposes into irreducible representations?) The physics of QCD, or the whole Standard Model? The reason why quantum field theory involves group representations? Etc.
            – G. Smith
            Nov 10 at 20:25




















          • Awesome do you have a any sources/papers/books I could find more about this?
            – Craig
            Nov 10 at 18:53










          • As well; in a universe where we had say, 4 or 5 colors and 8 gluons, how would this work?
            – Craig
            Nov 10 at 18:57






          • 1




            @Craig, are you familiar with representation theory? A big concept is that the same group can be "represented" with larger or smaller vector spaces. In this case, the quarks have the minimum number of vectors needed to realize SU(3) symmetry, and the gluons have (very loosely) that maximum number of vectors that can have the SU(3) symmetry, one for each dimension. If we had 4 colors, then we would instead want $4otimes bar 4 = 15oplus 1$, and we would have 15 gluon fields for the 4 colors.
            – Alex Meiburg
            Nov 10 at 19:01










          • The adjoint reprsentation of SU(n) has dimension $n^2-1$. So if you have 4 colors there need to be 15 gluons and if you have 5 colors there need to be 24 gluons.
            – G. Smith
            Nov 10 at 19:05










          • I’ll let others suggest the best references. But you need to clarify what you main interest is. The mathematics of representation theory? (For example, how do you figure out how an arbitrary product of irreducible representations decomposes into irreducible representations?) The physics of QCD, or the whole Standard Model? The reason why quantum field theory involves group representations? Etc.
            – G. Smith
            Nov 10 at 20:25


















          Awesome do you have a any sources/papers/books I could find more about this?
          – Craig
          Nov 10 at 18:53




          Awesome do you have a any sources/papers/books I could find more about this?
          – Craig
          Nov 10 at 18:53












          As well; in a universe where we had say, 4 or 5 colors and 8 gluons, how would this work?
          – Craig
          Nov 10 at 18:57




          As well; in a universe where we had say, 4 or 5 colors and 8 gluons, how would this work?
          – Craig
          Nov 10 at 18:57




          1




          1




          @Craig, are you familiar with representation theory? A big concept is that the same group can be "represented" with larger or smaller vector spaces. In this case, the quarks have the minimum number of vectors needed to realize SU(3) symmetry, and the gluons have (very loosely) that maximum number of vectors that can have the SU(3) symmetry, one for each dimension. If we had 4 colors, then we would instead want $4otimes bar 4 = 15oplus 1$, and we would have 15 gluon fields for the 4 colors.
          – Alex Meiburg
          Nov 10 at 19:01




          @Craig, are you familiar with representation theory? A big concept is that the same group can be "represented" with larger or smaller vector spaces. In this case, the quarks have the minimum number of vectors needed to realize SU(3) symmetry, and the gluons have (very loosely) that maximum number of vectors that can have the SU(3) symmetry, one for each dimension. If we had 4 colors, then we would instead want $4otimes bar 4 = 15oplus 1$, and we would have 15 gluon fields for the 4 colors.
          – Alex Meiburg
          Nov 10 at 19:01












          The adjoint reprsentation of SU(n) has dimension $n^2-1$. So if you have 4 colors there need to be 15 gluons and if you have 5 colors there need to be 24 gluons.
          – G. Smith
          Nov 10 at 19:05




          The adjoint reprsentation of SU(n) has dimension $n^2-1$. So if you have 4 colors there need to be 15 gluons and if you have 5 colors there need to be 24 gluons.
          – G. Smith
          Nov 10 at 19:05












          I’ll let others suggest the best references. But you need to clarify what you main interest is. The mathematics of representation theory? (For example, how do you figure out how an arbitrary product of irreducible representations decomposes into irreducible representations?) The physics of QCD, or the whole Standard Model? The reason why quantum field theory involves group representations? Etc.
          – G. Smith
          Nov 10 at 20:25






          I’ll let others suggest the best references. But you need to clarify what you main interest is. The mathematics of representation theory? (For example, how do you figure out how an arbitrary product of irreducible representations decomposes into irreducible representations?) The physics of QCD, or the whole Standard Model? The reason why quantum field theory involves group representations? Etc.
          – G. Smith
          Nov 10 at 20:25




















          draft saved

          draft discarded




















































          Thanks for contributing an answer to Physics Stack Exchange!


          • Please be sure to answer the question. Provide details and share your research!

          But avoid …



          • Asking for help, clarification, or responding to other answers.

          • Making statements based on opinion; back them up with references or personal experience.


          Use MathJax to format equations. MathJax reference.


          To learn more, see our tips on writing great answers.





          Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


          Please pay close attention to the following guidance:


          • Please be sure to answer the question. Provide details and share your research!

          But avoid …



          • Asking for help, clarification, or responding to other answers.

          • Making statements based on opinion; back them up with references or personal experience.


          To learn more, see our tips on writing great answers.




          draft saved


          draft discarded














          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f440142%2fdoes-it-really-make-sense-to-talk-about-the-color-of-gluons%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown





















































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown

































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown







          -

          這個網誌中的熱門文章

          Tangent Lines Diagram Along Smooth Curve

          圖片
          7 1 I am trying to replicate a diagram and have a minimal example. I don't know how to add additional tangents between the specified points and preserve smoothness. documentclass{article} usepackage{tikz} usetikzlibrary{calc,intersections} begin{document} begin{tikzpicture} % Axes draw [->, name path=x] (-1,0) -- (11,0) node [right] {$x$}; draw [->] (0,-1) -- (0,6) node [above] {$y$}; % Origin node at (0,0) [below left] {$0$}; % Points coordinate (start) at (1,-0.8); coordinate (c1) at (3,3); coordinate (c2) at (5.5,1.5); coordinate (c3) at (8,4); coordinate (end) at (10.5,-0.8); % show the points foreach n in {start,c1,c2,c3,end} fill [black] (n) circle (2pt) node [below] {}; % join the coordinates draw [thick,name path=curve] (start) to[out=70,in=180] (c1) to[out=0,in=180]
          閱讀完整內容

          Yusuf al-Mu'taman ibn Hud

          圖片
          Main article: Taifa of Zaragoza Al-Mu'taman Ruler of Zaragoza Reign 1081–1085 Predecessor Ahmad al-Muqtadir Successor Al-Mustain II Born Zaragoza Died 1085 Full name Yusuf ibn Ahmad al-Mu'taman ibn Hūd House Banu Hud Yusuf ibn Ahmad al-Mu'taman ibn Hūd (Arabic: المؤتمن بالله يوسف إبن أحمد إبن هود ‎, al-Mutaman bi l-Lah , died c. 1085) was the third king of the Banu Hud dynasty who ruled over the Taifa of Zaragoza from 1081 to 1085. Yusuf al-Mutaman reigned during the height of power of Muslim Zaragoza , following the thriving period of his father Ahmad al-Muqtadir. He continued his father's efforts and created around him a court of intellectuals, living in the beautiful palace of Aljafería, nicknamed as "the palace of joy". Al-Mu'taman was also a scholarly king and a patron of science, philosophy and arts. As an example of a wise king, he knew astrology, philosophy, and especially mathematics, a discipline in which
          閱讀完整內容

          Zucchini

          圖片
          This article is about the vegetable. For other uses, see Zucchini (disambiguation). Zucchini (courgette) A striped and a uniform color zucchini Genus Cucurbita Species Cucurbita pepo Origin 19th century northern Italy The zucchini ( / z uː ˈ k iː n i / , American English) or courgette ( / k ʊər ˈ ʒ ɛ t / , British English) is a summer squash which can reach nearly 1 metre (100 cm; 39 in) in length, but is usually harvested when still immature at about 15 to 25 cm (6 to 10 in). [1] A zucchini is a thin-skinned cultivar of what in Britain and Ireland is referred to as a marrow. [2] [3] In South Africa, a zucchini is known as a baby marrow. Along with certain other squashes and pumpkins, the zucchini belongs to the species Cucurbita pepo . It can be dark or light green. A related hybrid, the golden zucchini, is a deep yellow or orange color. [4] In a culinary context, the zucchini is treated as a vegetable; it is usually cooked and presented as a savory dish o
          閱讀完整內容