scholarly journals Generalized multiple-scalar field theory in Minkowski space-time free of Ostrogradski ghosts

2014 ◽  
Vol 90 (10) ◽  
Author(s):  
Vishagan Sivanesan
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Minkowski Space ◽  
Space Time ◽  
Scalar Field Theory ◽  
Minkowski Space Time

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 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.

Dimensional renormalization of scalar field theory in curved space-time

1980 ◽  
Vol 130 (1) ◽  
pp. 215-248 ◽  
Author(s):  
Lowell S Brown ◽  
John C Collins
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Space Time ◽  
Scalar Field Theory ◽  
Curved Space

scholarly journals Gravitation in Unified Scalar Field Theory

Universe ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 11
Author(s):  
Alexander A. Chernitskii
Keyword(s):  
Thin Film ◽  
Field Theory ◽  
Scalar Field ◽  
Field Model ◽  
Space Time ◽  
Two Dimensional ◽  
Scalar Field Theory ◽  
Fundamental Field ◽  
Practical Applications

The scalar field of space-time film is considered as unified fundamental field. The field model under consideration is the space-time generalization of the model for a two-dimensional thin film. The force and metrical interactions between solitons are considered. These interactions correspond to the electromagnetic and gravitational interactions respectively. The metrical interaction and its correspondence to the gravitational one are considered in detail. The practical applications of this approach are briefly discussed.

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