scholarly journals FIELD THEORY ON κ-MINKOWSKI SPACE REVISITED: NOETHER CHARGES AND BREAKING OF LORENTZ SYMMETRY

2008 ◽  
Vol 23 (18) ◽  
pp. 2687-2718 ◽  
Author(s):  
LAURENT FREIDEL ◽  
JERZY KOWALSKI-GLIKMAN ◽  
SEBASTIAN NOWAK
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Minkowski Space ◽  
Lorentz Invariance ◽  
Lorentz Symmetry ◽  
Space Time ◽  
Field Equations ◽  
Conserved Charges ◽  
Lorentz Scalar ◽  
Free Scalar

This paper is devoted to detailed investigations of free scalar field theory on κ-Minkowski space. After reviewing necessary mathematical tools, we discuss in detail the Lagrangian and solutions of field equations. We analyze the space–time symmetries of the model and construct the conserved charges associated with translational and Lorentz symmetries. We show that the version of the theory usually studied breaks Lorentz invariance in a subtle way: there is an additional trans-Planckian mode present, and an associated conserved charge (the number of such modes) is not a Lorentz scalar.

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.

scholarly journals Casimir effect in Horava–Lifshitz-like theories

2015 ◽  
Vol 30 (36) ◽  
pp. 1550220 ◽  
Author(s):  
I. J. Morales Ulion ◽  
E. R. Bezerra de Mello ◽  
A. Yu. Petrov
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Casimir Force ◽  
Casimir Effect ◽  
Lorentz Symmetry ◽  
Space Time ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Scalar Field Theory

In this paper, we consider a Lorentz-breaking scalar field theory within the Horava–Lifshtz approach. We investigate the changes that a space–time anisotropy produces in the Casimir effect. A massless real quantum scalar field is considered in two distinct situations: between two parallel plates and inside a rectangular two-dimensional box. In both cases, we have adopted specific boundary conditions on the field at the boundary. As we shall see, the energy and the Casimir force strongly depends on the parameter associated with the breaking of Lorentz symmetry and also on the boundary conditions.

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.

QUANTUM CYLINDRICAL WAVES AND PARAMETRIZED FIELD THEORY

2006 ◽  
Vol 15 (10) ◽  
pp. 1743-1752 ◽  
Author(s):  
MADHAVAN VARADARAJAN
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Quantum Gravity ◽  
Flat Space ◽  
Space Time ◽  
Gravitational Fields ◽  
Cylindrical Waves ◽  
Cylindrically Symmetric ◽  
Gravity Effects ◽  
Free Scalar

In this article, we review some illustrative results in the study of two related toy models for quantum gravity, namely cylindrical waves (which are cylindrically symmetric gravitational fields)and parametrized field theory (which is just free scalar field theory on a flat space–time in generally covariant disguise). In the former, we focus on the phenomenon of unexpected large quantum gravity effects in regions of weak classical gravitational fields and on an analysis of causality in a quantum geometry. In the latter, we focus on Dirac quantization, argue that this is related to the unitary implementability of free scalar field evolution along curved foliations of the flat space–time and review the relevant results for unitary implementability.

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

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