Ole Barndorff-Nielsen: Difference between revisions

Revision as of 00:16, 16 March 2013

In theoretical physics, specifically quantum field theory, Zamolodchikov's C-theorem states that there exists a positive real function, $C (g_{i}^{}, μ)$ , depending on the coupling constants of the quantum field theory considered, $g_{i}^{}$ , and on the energy scale, $μ_{}^{}$ , which has the following properties:

$C (g_{i}^{}, μ)$ decreases monotonically under the renormalization group (RG) flow.

At fixed points of the RG flow, which are specified by a set of fixed-point couplings $g_{i}^{*}$ , the function $C (g_{i}^{*}, μ) = C_{*}$ is a constant, independent of energy scale.

Alexander Zamolodchikov proved in 1986 that two-dimensional quantum field theory always has such a C-function. Moreover, at fixed points of the RG flow, which correspond to conformal field theories, Zamolodchikov's C-function is equal to the central charge of the corresponding conformal field theory,^[1] and roughly counts the degrees of freedom of the system.

Until recently, it had not been possible to prove an analog C-theorem in higher-dimensional quantum field theory. However, in 2011, Zohar Komargodski and Adam Schwimmer of the Weizmann Institute of Science proposed a proof for the physically more important four-dimensional case, which has gained acceptance.^[2]^[3] (Still, simultaneous monotonic and cyclic (limit cycle) or even chaotic RG flows are compatible with such flow functions when multivalued in the couplings, as evinced in specific systems.^[4]) RG flows of theories in 4 dimensions and the question of whether scale invariance implies conformal invariance, is a field of active research and not all questions are settled (circa 2013).

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

↑ Zamolodchikov, A. B. (1986). "Irreversibility" of the Flux of the Renormalization Group in a 2-D Field Theory, JETP Lett 43, pp 730–732.
↑ Template:Cite doi
↑ Template:Cite doi
↑ Template:Cite doi

[1] Zamolodchikov, A. B. (1986). "Irreversibility" of the Flux of the Renormalization Group in a 2-D Field Theory, JETP Lett 43, pp 730–732.

[2] Template:Cite doi

[komargodski-3] Template:Cite doi

[4] Template:Cite doi

[1]

[2]

[3]

[4]

@@ Line 1: / Line 1: @@
-The author is called Araceli Gulledge. Interviewing is what she does. Alabama is exactly where he and his wife reside and he has every thing that he needs there. Climbing is what adore performing.<br><br>my homepage - extended car warranty, [http://Holder11.Dothome.Co.kr/xe/center/733909 visit my web site],
+In [[theoretical physics]], specifically [[quantum field theory]], Zamolodchikov's  '''C-theorem''' states that there exists a positive real function, <math>C(g^{}_i,\mu)</math>, depending on the [[coupling constant]]s of the quantum field theory considered, <math>g^{}_i</math>, and on the energy scale, <math>\mu^{}_{}</math>, which has the following properties:
+*<math>C(g^{}_i,\mu)</math> decreases monotonically under the [[renormalization group]] (RG) flow.
+*At fixed points of the RG flow, which are specified by a set of fixed-point couplings <math>g^*_i</math>, the function <math>C(g^*_i,\mu)=C_*</math> is a constant, independent of energy scale.
+[[Alexander Zamolodchikov]] proved in 1986 that two-dimensional quantum field theory always has such a ''C''-function. Moreover, at fixed points of the RG flow, which correspond to [[conformal field theory|conformal field theories]], Zamolodchikov's ''C''-function is equal to the [[central charge]] of the corresponding conformal field theory,<ref>[[Alexander Zamolodchikov|Zamolodchikov, A. B.]] (1986).  [http://www.jetpletters.ac.ru/ps/1413/article_21504.pdf "Irreversibility" of the Flux of the Renormalization Group in a 2-D Field Theory], ''JETP Lett'' '''43''', pp 730–732.</ref> and roughly counts the degrees of freedom of the system.
+Until recently, it had not been possible to prove an analog ''C''-theorem in higher-dimensional quantum field theory.  However, in 2011, Zohar Komargodski and Adam Schwimmer of the [[Weizmann Institute of Science]] proposed a proof for the physically more important four-dimensional case, which has gained acceptance.<ref>{{cite doi| 10.1038/nature.2011.9352|noedit}}</ref><ref name="komargodski">{{cite doi|10.1007/JHEP12(2011)099|noedit}}</ref> (Still, simultaneous monotonic and cyclic ([[limit cycle]]) or even chaotic RG flows are compatible with such flow functions when multivalued in the couplings, as evinced in specific systems.<ref>{{cite doi|10.1103/PhysRevLett.108.131601|noedit}}</ref>) RG flows of theories in 4 dimensions and the question of whether scale invariance implies conformal invariance, is a field of active research and not all questions are settled (circa 2013).
+==See also==
+*[[Conformal field theory]]
+==References==
+{{reflist}}
+[[Category:Conformal field theory]]
+[[Category:Renormalization group]]
+[[Category:Quantum field theory]]
+[[Category:Theoretical physics]]
+[[Category:Mathematical physics]]

Ole Barndorff-Nielsen: Difference between revisions

Revision as of 00:16, 16 March 2013

See also

References

Navigation menu

Search