scholarly journals STAR PRODUCT AND INTERACTING FIELDS ON κ-MINKOWSKI SPACE

2009 ◽  
Vol 24 (28) ◽  
pp. 2243-2250 ◽  
Author(s):  
JERZY KOWALSKI-GLIKMAN ◽  
ADRIAN WALKUS
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Minkowski Space ◽  
Star Product ◽  
Leading Order ◽  
Scalar Field Theory ◽  
Interaction Term ◽  
Explicit Expressions

In this note we extend the methods developed by Freidel et al.20 to derive the form of ϕ4 interaction term in the case of scalar field theory on κ-Minkowski space, defined in terms of star product. We present explicit expressions for the κ-Minkowski star product. Having obtained the the interaction term we use the resulting deformed conservation rules to investigate if they lead to any threshold anomaly, and we find that in the leading order they do not, as expected.

scholarly journals SCALAR FIELD THEORY ON κ-MINKOWSKI SPACE–TIME AND TRANSLATION AND LORENTZ INVARIANCE

2011 ◽  
Vol 26 (07n08) ◽  
pp. 1439-1468 ◽  
Author(s):  
S. MELJANAC ◽  
A. SAMSAROV
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Minkowski Space ◽  
Lorentz Invariance ◽  
Star Product ◽  
Space Time ◽  
Scalar Field Theory ◽  
Operator Representation ◽  
Minkowski Space Time ◽  
Deformed Algebra

We investigate the properties of κ-Minkowski space–time by using representations of the corresponding deformed algebra in terms of undeformed Heisenberg–Weyl algebra. The deformed algebra consists of κ-Poincaré algebra extended with the generators of the deformed Weyl algebra. The part of deformed algebra, generated by rotation, boost and momentum generators, is described by the Hopf algebra structure. The approach used in our considerations is completely Lorentz covariant. We further use an advantage of this approach to consistently construct a star product, which has a property that under integration sign, it can be replaced by a standard pointwise multiplication, a property that was since known to hold for Moyal but not for κ-Minkowski space–time. This star product also has generalized trace and cyclic properties, and the construction alone is accomplished by considering a classical Dirac operator representation of deformed algebra and requiring it to be Hermitian. We find that the obtained star product is not translationally invariant, leading to a conclusion that the classical Dirac operator representation is the one where translation invariance cannot simultaneously be implemented along with hermiticity. However, due to the integral property satisfied by the star product, noncommutative free scalar field theory does not have a problem with translation symmetry breaking and can be shown to reduce to an ordinary free scalar field theory without nonlocal features and tachyonic modes and basically of the very same form. The issue of Lorentz invariance of the theory is also discussed.

DISSIPATIVE SCALAR FIELD THEORY VIA DEFORMATION QUANTIZATION

2013 ◽  
Vol 28 (16) ◽  
pp. 1350068
Author(s):  
ILIANA CARRILLO-IBARRA ◽  
HUGO GARCÍA-COMPEÁN ◽  
FRANCISCO J. TURRUBIATES
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Deformation Quantization ◽  
Star Product ◽  
Quantum Mechanical ◽  
Expectation Values ◽  
Scalar Field Theory ◽  
Oscillation Modes ◽  
Quantization Formalism ◽  
Damped Oscillation

The dissipative scalar field theory by means of the deformation quantization formalism is studied. Following the ideas presented by G. Dito and F. J. Turrubiates [Phys. Lett. A352, 309 (2006)] for quantum mechanics, a star product which contains the dissipative effect for the damped oscillation modes of the field is constructed. Employing this approach the expectation values of some observables in the quantum mechanical case as well as certain correlation functions for the field case are obtained under a particular dissipative process.

scholarly journals COMPLEX q-ANALYSIS AND SCALAR FIELD THEORY ON A q-LATTICE

1994 ◽  
Vol 09 (12) ◽  
pp. 1121-1130 ◽  
Author(s):  
MARCELO R. UBRIACO
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Minkowski Space ◽  
Function Space ◽  
Laplace Equation ◽  
Difference Equations ◽  
Second Order ◽  
Inner Product ◽  
Two Dimensional ◽  
Scalar Field Theory

We develop the basic formalism of complex q-analysis to study the solutions of second order q-difference equations which reduce, in the q → 1 limit, to the ordinary Laplace equation in Euclidean and Minkowski space. After defining an inner product on the function space we construct and study the properties of the solutions, and then apply this formalism to the Schrödinger equation and two-dimensional scalar field theory.

scholarly journals A short introduction to κ-deformation

2017 ◽  
Vol 32 (35) ◽  
pp. 1730026 ◽  
Author(s):  
J. Kowalski-Glikman
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Minkowski Space ◽  
Momentum Space ◽  
Short Review ◽  
Short Introduction ◽  
Scalar Field Theory ◽  
Poincaré Algebra ◽  
Free Scalar

In this short review we describe some aspects of [Formula: see text]-deformation. After discussing the algebraic and geometric approaches to [Formula: see text]-Poincaré algebra we construct the free scalar field theory, both on noncommutative [Formula: see text]-Minkowski space and on curved momentum space. Finally, we make a few remarks concerning the interacting scalar field.

scholarly journals Renormalization group approach for Lorentz-violating scalar field theory at all loop orders

2016 ◽  
Vol 13 (04) ◽  
pp. 1650049 ◽  
Author(s):  
William de Carvalho Vieira ◽  
Paulo Renato Silva de Carvalho
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Feynman Diagrams ◽  
Mathematical Explanation ◽  
Leading Order ◽  
Group Approach ◽  
Scalar Field Theory ◽  
Massless Theory ◽  
Renormalization Group Approach ◽  
Proof By Induction

We compute, both explicitly, at least, up to next-to-leading order and in a proof by induction for all loop levels, the critical exponents for thermal Lorentz-violating O([Formula: see text]) self-interacting scalar field theory. They are evaluated in a massless theory renormalized at arbitrary external momenta, where a reduced number of Feynman diagrams is needed. The results are presented and shown to be identical to that found previously in distinct theories renormalized at different renormalization schemes. Finally, we give both mathematical explanation and physical interpretation for them based on coordinates redefinition techniques and symmetry ideas, respectively.

scholarly journals Scalar field theory limits of bosonic string amplitudes

2000 ◽  
Vol 579 (1-2) ◽  
pp. 379-410 ◽  
Author(s):  
Alberto Frizzo ◽  
Lorenzo Magnea ◽  
Rodolfo Russo
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Bosonic String ◽  
Scalar Field Theory ◽  
String Amplitudes

On causality in polymer scalar field theory

2011 ◽  
Author(s):  
Angel A. García-Chung ◽  
Hugo A. Morales-Técotl ◽  
Luis Arturo Ureña-López ◽  
Hugo Aurelio Morales-Técotl ◽  
Román Linares-Romero ◽  
...  
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Scalar Field Theory

scholarly journals ASYMPTOTIC FREEDOM IN A SCALAR FIELD THEORY ON THE LATTICE

1998 ◽  
Vol 13 (31) ◽  
pp. 2495-2501 ◽  
Author(s):  
KURT LANGFELD ◽  
HUGO REINHARDT
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Scalar Particle ◽  
Higgs Sector ◽  
Asymptotic Freedom ◽  
Scalar Field Theory ◽  
Large N ◽  
The Standard Model ◽  
Conceptual Problems ◽  
The Continuum

A scalar field theory in four space–time dimensions is proposed, which embodies a scalar condensate, but is free of the conceptual problems of standard ϕ4-theory. We propose an N-component, O(N)-symmetric scalar field theory, which is originally defined on the lattice. The scalar lattice model is analytically solved in the large-N limit. The continuum limit is approached via an asymptotically free scaling. The renormalized theory evades triviality, and furthermore gives rise to a dynamically formed mass of the scalar particle. The model might serve as an alternative to the Higgs sector of the standard model, where the quantum level of the standard ϕ4-theory contradicts phenomenology due to triviality.

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