scholarly journals NONCOMMUTATIVE THERMOFIELD DYNAMICS

2010 ◽  
Vol 25 (16) ◽  
pp. 3209-3220 ◽  
Author(s):  
MARCELO L. COSTA ◽  
AMILCAR R. QUEIROZ ◽  
ADEMIR E. SANTANA
Keyword(s):  
Field Theories ◽  
Effect Of Temperature ◽  
Integral Approach ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Point Function ◽  
Operator Formalism ◽  
Noncommutative Spaces ◽  
The One ◽  
Noncommutative Parameter

The real-time operator formalism for thermal quantum field theories, thermofield dynamics, is formulated in terms of a path-integral approach in noncommutative spaces. As an application, the two-point function for a thermal noncommutative λϕ4 theory is derived at the one-loop level. The effect of temperature and the noncommutative parameter, competing with one another, is analyzed.

DOES STOCHASTIC ANALYTIC REGULARIZATION PROVIDE QUANTUM FIELD THEORIES?

1992 ◽  
Vol 07 (04) ◽  
pp. 777-794
Author(s):  
C. P. MARTIN
Keyword(s):  
Field Theory ◽  
Regularization Method ◽  
Gauge Theories ◽  
Field Theories ◽  
Intermediate Step ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Point Function ◽  
Four Dimensions ◽  
Analytic Regularization

We analyze whether the so-called method of stochastic analytic regularization is suitable as an intermediate step for constructing perturbative renormalized quantum field theories. We choose a λϕ3 in six dimensions to prove that this regularization method does not in general provide a quantum field theory. This result seems to apply to any field theory with a quadratically UV-divergent stochastic two-point function, for instance λϕ4 and gauge theories in four dimensions.

scholarly journals PERTURBATIVE SYMMETRIES ON NONCOMMUTATIVE SPACES

2004 ◽  
Vol 19 (32) ◽  
pp. 5693-5706 ◽  
Author(s):  
CHRISTIAN BLOHMANN
Keyword(s):  
Field Theory ◽  
Lie Algebras ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Plane ◽  
Star Products ◽  
Quantum Field ◽  
Enveloping Algebras ◽  
Noncommutative Spaces ◽  
Noncommutative Quantum

Perturbative deformations of symmetry structures on noncommutative spaces are studied in view of noncommutative quantum field theories. The rigidity of enveloping algebras of semisimple Lie algebras with respect to formal deformations is reviewed in the context of star products. It is shown that rigidity of symmetry algebras extends to rigidity of the action of the symmetry on the space. This implies that the noncommutative spaces considered can be realized as star products by particular ordering prescriptions which are compatible with the symmetry. These symmetry preserving ordering prescriptions are calculated for the quantum plane and four-dimensional quantum Euclidean space. The result can be used to construct invariant Lagrangians for quantum field theory on noncommutative spaces with a deformed symmetry.

scholarly journals SUBFACTORS AND 1+1-DIMENSIONAL TQFTs

2007 ◽  
Vol 18 (01) ◽  
pp. 69-112 ◽  
Author(s):  
VIJAY KODIYALAM ◽  
VISHWAMBHAR PATI ◽  
V. S. SUNDER
Keyword(s):  
The Other ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Planar Algebras ◽  
Topological Quantum ◽  
The One ◽  
Topological Quantum Field Theories

We construct a certain "cobordism category" [Formula: see text] whose morphisms are suitably decorated cobordism classes between similarly decorated closed oriented 1-manifolds, and show that there is essentially a bijection between (1+1-dimensional) unitary topological quantum field theories (TQFTs) defined on [Formula: see text], on the one hand, and Jones' subfactor planar algebras, on the other.

scholarly journals TWISTED QUANTUM FIELDS ON MOYAL AND WICK–VOROS PLANES ARE INEQUIVALENT

2009 ◽  
Vol 24 (22) ◽  
pp. 1721-1730 ◽  
Author(s):  
A. P. BALACHANDRAN ◽  
M. MARTONE
Keyword(s):  
Field Theories ◽  
Gauge Fields ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Poincaré Group ◽  
Energy Diagram ◽  
Poincare Group ◽  
Self Energy ◽  
Moyal Plane ◽  
Noncommutative Parameter

The Moyal and Wick–Voros planes [Formula: see text] are *-isomorphic. On each of these planes the Poincaré group acts as a Hopf algebra symmetry if its coproducts are deformed by twist factors [Formula: see text]. We show that the *-isomorphism [Formula: see text] also does not map the corresponding twists of the Poincaré group algebra. The quantum field theories on these planes with twisted Poincaré–Hopf symmetries are thus inequivalent. We explicitly verify this result by showing that a nontrivial dependence on the noncommutative parameter is present for the Wick–Voros plane in a self-energy diagram whereas it is known to be absent on the Moyal plane (in the absence of gauge fields).1–3 Our results differ from those of Ref. 4 because of differences in the treatments of quantum field theories.

ANOMALIES AT FINITE TEMPERATURE AND DENSITY

1994 ◽  
Vol 09 (09) ◽  
pp. 1423-1442 ◽  
Author(s):  
A. GÓMEZ NICOLA ◽  
R. F. ALVAREZ-ESTRADA
Keyword(s):  
Analytic Continuation ◽  
Finite Temperature ◽  
Arbitrary Number ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Zero Temperature ◽  
Functional Methods ◽  
Abelian Case ◽  
The One

Chiral anomalies for Abelian and non-Abelian quantum field theories at finite temperature and density (FTFD) are analyzed in detail in both imaginary and real time (IT and RT) formalisms. IT and RT triangle diagrams and IT functional methods (à la Fujikawa) are used at FTFD. The vector anomaly (the one regarding the lepton and baryon numbers) in the Weinberg–Salam theory, for an arbitrary number of fermion families, is also treated using IT functional methods at FTFD. In all cases, the expressions for the FTFD anomalies (as functions of the corresponding quantities) turn out to be identical to those at zero temperature and density, thereby extending previous results by various authors for the finite temperature and zero density case. Moreover, the independence of anomalies from temperature and density is shown to be consistent, at least in the Abelian case, with the analytic continuation from the IT formulation to the RT one.

MASS RENORMALIZATION IN A HAMILTONIAN APPROACH

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4643-4670 ◽  
Author(s):  
AXEL WEBER
Keyword(s):  
Perturbation Theory ◽  
Relativistic Quantum ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Hamiltonian Approach ◽  
Mass Renormalization ◽  
Regularization Scheme ◽  
The One

We consider the energies of the one-particle states of relativistic quantum field theories in old-fashioned perturbation theory, and treat their regularization and renormalization from a strictly Hamiltonian perspective. We show that the one-loop diagrams lead to the renormalization of the mass for bosons and fermions identically to covariant perturbation theory, provided an appropriate regularization scheme is used. In particular, we show that a naive spatial momentum cutoff breaks covariance (in the limit where the cutoff is removed) in the case of the one-fermion states.

scholarly journals a×b=c in 2+1D TQFT

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 468
Author(s):  
Matthew Buican ◽  
Linfeng Li ◽  
Rajath Radhakrishnan
Keyword(s):  
Gauge Theories ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Mathieu Group ◽  
Gauge Groups ◽  
Global Properties ◽  
Topological Quantum ◽  
The One ◽  
Chern Simons

We study the implications of the anyon fusion equation a×b=c on global properties of 2+1D topological quantum field theories (TQFTs). Here a and b are anyons that fuse together to give a unique anyon, c. As is well known, when at least one of a and b is abelian, such equations describe aspects of the one-form symmetry of the theory. When a and b are non-abelian, the most obvious way such fusions arise is when a TQFT can be resolved into a product of TQFTs with trivial mutual braiding, and a and b lie in separate factors. More generally, we argue that the appearance of such fusions for non-abelian a and b can also be an indication of zero-form symmetries in a TQFT, of what we term "quasi-zero-form symmetries" (as in the case of discrete gauge theories based on the largest Mathieu group, M24), or of the existence of non-modular fusion subcategories. We study these ideas in a variety of TQFT settings from (twisted and untwisted) discrete gauge theories to Chern-Simons theories based on continuous gauge groups and related cosets. Along the way, we prove various useful theorems.

scholarly journals A bound on thermal relativistic correlators at large spacelike momenta

2020 ◽  
Vol 8 (4) ◽  
Author(s):  
Souvik Banerjee ◽  
Kyriakos Papadodimas ◽  
Suvrat Raju ◽  
Prasant Samantray ◽  
Pushkal Shrivastava
Keyword(s):  
Field Theory ◽  
Relativistic Quantum ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Relativistic Quantum Field Theory ◽  
Point Function ◽  
Open Problems ◽  
Perturbative Quantum ◽  
Free Fields

We consider thermal Wightman correlators in a relativistic quantum field theory in the limit where the spatial momenta of the insertions become large while their frequencies stay fixed. We show that, in this limit, the size of these correlators is bounded by e^{-\beta R}e−βR, where RR is the radius of the smallest sphere that contains the polygon formed by the momenta. We show that perturbative quantum field theories can saturate this bound through suitably high-order loop diagrams. We also consider holographic theories in dd-spacetime dimensions, where we show that the leading two-point function of generalized free-fields saturates the bound in d = 2d=2 and is below the bound for d > 2d>2. We briefly discuss interactions in holographic theories and conclude with a discussion of several open problems.

scholarly journals FUNCTIONAL BOSONIZATION WITH TIME DEPENDENT PERTURBATIONS

2004 ◽  
Vol 19 (29) ◽  
pp. 4953-4971 ◽  
Author(s):  
CARLOS M. NAÓN ◽  
MARIANO J. SALVAY ◽  
MARTA L. TROBO
Keyword(s):  
Energy Density ◽  
Time Dependent ◽  
Field Theories ◽  
Integral Approach ◽  
Electronic Systems ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Zero Temperature ◽  
Total Energy Density ◽  
Luttinger Model

We extend a path-integral approach to bosonization previously developed in the framework of equilibrium Quantum Field Theories, to the case in which time-dependent interactions are taken into account. In particular we consider a noncovariant version of the Thirring model in the presence of a dynamic barrier at zero temperature. By using the Closed Time Path (Schwinger–Keldysh) formalism, we compute the Green's function and the Total Energy Density of the system. Since our model contains the Tomonaga–Luttinger model as a particular case, we make contact with recent results on nonequilibrium electronic systems.

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