Quantization of the self-dual Yang-Mills system: Exchange algebras and local quantum group in four-dimensional quantum field theories

1993 ◽  
Vol 70 (13) ◽  
pp. 1916-1919 ◽  
Author(s):  
Ling-Lie Chau ◽  
Itaru Yamanaka
Keyword(s):  
Quantum Group ◽  
The Self ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Yang Mills ◽  
Local Quantum

RAINBOW STATISTICS

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4623-4641 ◽  
Author(s):  
MICHELE ARZANO ◽  
DARIO BENEDETTI
Keyword(s):  
Quantum Group ◽  
Hilbert Spaces ◽  
Group Symmetry ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Additional Structure ◽  
Local Quantum ◽  
Group Symmetries ◽  
Noncommutative Quantum

Noncommutative quantum field theories and their global quantum group symmetries provide an intriguing attempt to go beyond the realm of standard local quantum field theory. A common feature of these models is that the quantum group symmetry of their Hilbert spaces induces additional structure in the multiparticle states which reflects a nontrivial momentum-dependent statistics. We investigate the properties of this "rainbow statistics" in the particular context of κ-quantum fields and discuss the analogies/differences with models with twisted statistics.

scholarly journals ON GENERALIZED SELF-DUALITY EQUATIONS TOWARDS SUPERSYMMETRIC QUANTUM FIELD THEORIES OF FORMS

1998 ◽  
Vol 13 (14) ◽  
pp. 1115-1132 ◽  
Author(s):  
LAURENT BAULIEU ◽  
CÉLINE LAROCHE
Keyword(s):  
The Self ◽  
Field Theories ◽  
Gauge Fields ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Time Dimension ◽  
Yang Mills ◽  
Self Duality ◽  
Topological Quantum ◽  
Gauge Functions

We classify possible "self-duality" equations for p-form gauge fields in space–time dimension up to D=16, generalizing the pioneering work of Corrigan et al. (1982) on Yang–Mills fields (p=1) in 4<D≤8. We impose two crucial requirements. First, there should exist a 2(p+1)-form T-invariant under a subgroup H of SO D. Second, the representation for the SO D curvature of the gauge field must decompose under H in a relevant way. When these criteria are fulfilled, the "self-duality" equations can be candidates of gauge functions for SO D-covariant and H-invariant topological quantum field theories. Intriguing possibilities occur for D≥10 for various p-form gauge fields.

scholarly journals A thermodynamic origin for the Cohen-Kaplan-Nelson bound

2021 ◽  
Author(s):  
Satish Ramakrishna
Keyword(s):  
General Relativity ◽  
Free Energy ◽  
Equation Of State ◽  
Density Of States ◽  
Canonical Ensemble ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Local Quantum ◽  
The Universe

Abstract The Cohen-Kaplan-Nelson bound is imposed on the grounds of logical consistency (with classical General Relativity) upon local quantum field theories. This paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. This is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. The paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.

scholarly journals THE RELATIONS BETWEEN GENERALIZED FIELDS AND SUPERFIELDS FORMALISMS OF THE BATALIN–VILKOVISKY METHOD OF QUANTIZATION

2004 ◽  
Vol 19 (14) ◽  
pp. 2339-2353 ◽  
Author(s):  
ÖMER F. DAYI
Keyword(s):  
General Solution ◽  
Master Equation ◽  
Gauge Theories ◽  
Relativistic Particle ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Yang Mills ◽  
Topological Quantum ◽  
Topological Quantum Field Theories

A general solution of the Batalin–Vilkovisky master equation was formulated in terms of generalized fields. Recently, a superfields approach of obtaining solutions of the Batalin–Vilkovisky master equation is also established. Superfields formalism is usually applied to topological quantum field theories. However, generalized fields method is suitable to find solutions of the Batalin–Vilkovisky master equation either for topological quantum field theories or the usual gauge theories like Yang–Mills theory. We show that by truncating some components of superfields with appropriate actions, generalized fields formalism of the usual gauge theories result. We demonstrate that for some topological quantum field theories and the relativistic particle both of the methods possess the same field contents and yield similar results. Inspired by the observed relations, we give the solution of the BV master equation for on-shell N=1 supersymmetric Yang–Mills theory utilizing superfields.

The light-cone gauge

1986 ◽  
Vol 64 (5) ◽  
pp. 624-632 ◽  
Author(s):  
H. C. Lee
Keyword(s):  
Quantum Chromodynamics ◽  
Quantum Electrodynamics ◽  
Light Cone ◽  
Field Theories ◽  
Special Role ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Kaluza Klein

Some aspects of recent development in the light-cone gauge and its special role in quantum-field theories are reviewed. Topics discussed include the two- and four-component formulations of the light-cone gauge, Slavnov–Taylor and Becchi– Rouet–Stora identities, quantum electrodynamics, quantum chromodynamics, renormalization of Yang–Mills theory and supersymmetric theory, gravity, and the quantum-induced compactification of Kaluza–Klein theories in the light-cone gauge.

scholarly journals LECTURE NOTES ON INTERACTING QUANTUM FIELDS IN DE SITTER SPACE

2014 ◽  
Vol 23 (01) ◽  
pp. 1430001 ◽  
Author(s):  
E. T. AKHMEDOV
Keyword(s):  
De Sitter Space ◽  
The Self ◽  
Field Theories ◽  
Tree Level ◽  
Main Concern ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Quantum Fields ◽  
De Sitter ◽  
Invariant States

We discuss peculiarities of quantum fields in de Sitter (dS) space on the example of the self-interacting massive real scalar, minimally coupled to the gravity background. Nonconformal quantum field theories (QFTs) in dS space show very special infrared behavior, which is not shared by quantum fields neither in flat nor in anti-dS space: in dS space loops are not suppressed in comparison with tree level contributions because there are strong infrared corrections. That is true even for massive fields. Our main concern is the interrelation between these infrared effects, the invariance of the QFT under the dS isometry and the (in)stability of dS invariant states (and of dS space itself) under nonsymmetric perturbations.

scholarly journals A thermodynamic origin for the Cohen-Kaplan-Nelson bound

2021 ◽  
Author(s):  
Satish Ramakrishna
Keyword(s):  
General Relativity ◽  
Free Energy ◽  
Equation Of State ◽  
Density Of States ◽  
Canonical Ensemble ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Local Quantum ◽  
The Universe

Abstract The Cohen-Kaplan-Nelson bound is imposed on the grounds of logical consistency (with classical General Relativity) upon local quantum field theories. This paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. This is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. The paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.

⋆-cohomology, third type Chern character and anomalies in general translation-invariant noncommutative Yang–Mills

2021 ◽  
pp. 2150089
Author(s):  
Amir Abbass Varshovi
Keyword(s):  
Chern Character ◽  
Adjoint Action ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Translation Invariant ◽  
Yang Mills ◽  
Noncommutative Version ◽  
General Translation ◽  
Noncommutative Quantum

A representation of general translation-invariant star products ⋆ in the algebra of [Formula: see text] is introduced which results in the Moyal–Weyl–Wigner quantization. It provides a matrix model for general translation-invariant noncommutative quantum field theories in terms of the noncommutative calculus on differential graded algebras. Upon this machinery a cohomology theory, the so-called ⋆-cohomology, with groups [Formula: see text], [Formula: see text], is worked out which provides a cohomological framework to formulate general translation-invariant noncommutative quantum field theories based on the achievements for the commutative fields, and is comparable to the Seiberg–Witten map for the Moyal case. Employing the Chern–Weil theory via the integral classes of [Formula: see text] a noncommutative version of the Chern character is defined as an equivariant form which contains topological information about the corresponding translation-invariant noncommutative Yang–Mills theory. Thereby, we study the mentioned Yang–Mills theories with three types of actions of the gauge fields on the spinors, the ordinary, the inverse, and the adjoint action, and then some exact solutions for their anomalous behaviors are worked out via employing the homotopic correlation on the integral classes of ⋆-cohomology. Finally, the corresponding consistent anomalies are also derived from this topological Chern character in the ⋆-cohomology.

Sign in / Sign up

Export Citation Format

Share Document