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 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 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 Entanglement growth after a global quench in free scalar field theory

2016 ◽  
Vol 2016 (11) ◽  
Author(s):  
Jordan S. Cotler ◽  
Mark P. Hertzberg ◽  
Márk Mezei ◽  
Mark T. Mueller
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Scalar Field Theory ◽  
Free Scalar
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