scholarly journals Thermal Ground State and Nonthermal Probes

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Thierry Grandou ◽  
Ralf Hofmann
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Ground State ◽  
Topological Charge ◽  
Classical Equation ◽  
Coarse Graining ◽  
Equation Of Motion ◽  
Quantum Field ◽  
Electric Permittivity ◽  
Yang Mills

The Euclidean formulation of SU(2) Yang-Mills thermodynamics admits periodic, (anti)self-dual solutions to the fundamental, classical equation of motion which possess one unit of topological charge: (anti)calorons. A spatial coarse graining over the central region in a pair of such localised field configurations with trivial holonomy generates an inert adjoint scalar fieldϕ, effectively describing the pure quantum part of the thermal ground state in the induced quantum field theory. Here we show for the limit of zero holonomy how (anti)calorons associate a temperature independent electric permittivity and magnetic permeability to the thermal ground state ofSU2CMB, the Yang-Mills theory conjectured to underlie the fundamental description of thermal photon gases.

scholarly journals DIFFERENTIAL GEOMETRY FROM QUANTUM FIELD THEORY

2013 ◽  
Vol 10 (04) ◽  
pp. 1350003
Author(s):  
W. F. CHEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Differential Geometry ◽  
Historical Development ◽  
Theoretical Physics ◽  
Quantum Field ◽  
Yang Mills ◽  
And Mathematics

We review the historical development and physical ideas of topological Yang–Mills theory and explain how quantum field theory, a physical framework describing subatomic physics, can be used as a tool to study differential geometry. We further emphasize that this phenomenon demonstrates that the inter-relation between theoretical physics and mathematics have come into a new stage.

scholarly journals Broken Symmetry and Yang–Mills Theory

2014 ◽  
Vol 03 (01) ◽  
pp. 54-67 ◽  
Author(s):  
François Englert
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Statistical Physics ◽  
Broken Symmetry ◽  
Quantum Field ◽  
Yang Mills

From its inception in statistical physics to its role in the construction and in the development of the asymmetric Yang–Mills phase in quantum field theory, the notion of spontaneous broken symmetry permeates contemporary physics. This is reviewed with particular emphasis on the conceptual issues.

THE FIRST DONALDSON INVARIANT AS THE WINDING NUMBER OF A NICOLAI MAP

1988 ◽  
Vol 03 (17) ◽  
pp. 1647-1650 ◽  
Author(s):  
P. MANSFIELD
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Partition Function ◽  
Relativistic Quantum ◽  
Quantum Field ◽  
Winding Number ◽  
Relativistic Quantum Field Theory ◽  
Yang Mills ◽  
Stochastic Map

We show that the first Donaldson invariant expressed by Witten as the partition function of a relativistic quantum field theory can be interpreted as the winding number of the stochastic map introduced by Nicolai in the context of supersymmetric Yang-Mills theories.

scholarly journals Area-Dependent Quantum Field Theory

2020 ◽  
Author(s):  
Ingo Runkel ◽  
Lóránt Szegedy
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Two Dimensional ◽  
Positive Real ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Frobenius Algebras ◽  
Topological Quantum ◽  
Topological Theories

AbstractArea-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail.

scholarly journals Linear Yang–Mills Theory as a Homotopy AQFT

2019 ◽  
Vol 378 (1) ◽  
pp. 185-218 ◽  
Author(s):  
Marco Benini ◽  
Simen Bruinsma ◽  
Alexander Schenkel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Poisson Structure ◽  
Gauge Fields ◽  
Quantum Field ◽  
Lorentzian Manifolds ◽  
Algebraic Quantum Field Theory ◽  
Yang Mills ◽  
Algebraic Quantum ◽  
Klein Gordon

AbstractIt is observed that the shifted Poisson structure (antibracket) on the solution complex of Klein–Gordon and linear Yang–Mills theory on globally hyperbolic Lorentzian manifolds admits retarded/advanced trivializations (analogs of retarded/advanced Green’s operators). Quantization of the associated unshifted Poisson structure determines a unique (up to equivalence) homotopy algebraic quantum field theory (AQFT), i.e. a functor that assigns differential graded $$*$$ ∗ -algebras of observables and fulfills homotopical analogs of the AQFT axioms. For Klein–Gordon theory the construction is equivalent to the standard one, while for linear Yang–Mills it is richer and reproduces the BRST/BV field content (gauge fields, ghosts and antifields).

scholarly journals INFRARED ANALYSIS OF QUANTUM FIELD THEORIES

2007 ◽  
Vol 22 (08n09) ◽  
pp. 1727-1734 ◽  
Author(s):  
MARCO FRASCA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Asymptotic Series ◽  
Field Theories ◽  
Infrared Analysis ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Strongly Coupled ◽  
Yang Mills ◽  
The Given

We show that for a λϕ4 theory having many components, the solution with all equal components in the infrared regime is stable with respect to our expansion given by a recently devised approach to analyze strongly coupled quantum field theory. The analysis is extended to a pure Yang–Mills theory showing how, in this case, the given asymptotic series exists. In this way, many components theories in the infrared regime can be mapped to a single component scalar field theory obtaining their spectrum.

scholarly journals Classical instanton solutions in quantum field theory

2020 ◽  
pp. 78-85
Author(s):  
Roman G. Shulyakovsky ◽  
Alexander S. Gribowsky ◽  
Alexander S. Garkun ◽  
Maxim N. Nevmerzhitsky ◽  
Alexei O. Shaplov ◽  
...  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Yukawa Potential ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Quantum Field ◽  
Two Dimensional ◽  
Yang Mills ◽  
The One

Instantons are non-trivial solutions of classical Euclidean equations of motion with a finite action. They provide stationary phase points in the path integral for tunnel amplitude between two topologically distinct vacua. It make them useful in many applications of quantum theory, especially for describing the wave function of systems with a degenerate vacua in the framework of the path integrals formalism. Our goal is to introduce the current situation about research on instantons and prepare for experiments. In this paper we give a review of instanton effects in quantum theory. We find in stanton solutions in some quantum mechanical problems, namely, in the problems of the one-dimensional motion of a particle in two-well and periodic potentials. We describe known instantons in quantum field theory that arise, in particular, in the two-dimensional Abelian Higgs model and in SU(2) Yang – Mills gauge fields. We find instanton solutions of two-dimensional scalar field models with sine-Gordon and double-well potentials in a limited spatial volume. We show that accounting of instantons significantly changes the form of the Yukawa potential for the sine-Gordon model in two dimensions.

Dynamical derivation of the Yang–Mills S-matrix

1982 ◽  
Vol 60 (11) ◽  
pp. 1630-1640
Author(s):  
Robert E. Pugh
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Matrix Equation ◽  
Quantum Field ◽  
Yang Mills ◽  
Covariant Quantum ◽  
S Matrix ◽  
Feynman Rules

The Feynman rules for self-interacting Yang–Mills fields are derived within the framework of conventional covariant quantum field theory by explicitly calculating the contributions of the nonphysical field components to the violations of the S-matrix equation of continuity.

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