scholarly journals A NOTE ON THE IMPLEMENTATION OF POINCARÉ SYMMETRY IN NONCOMMUTATIVE FIELD THEORY

2010 ◽  
Vol 25 (31) ◽  
pp. 5747-5764
Author(s):  
IGNACIO CORTESE ◽  
J. ANTONIO GARCÍA
Keyword(s):  
Field Theory ◽  
Star Product ◽  
Space Time ◽  
Noncommutative Field Theory ◽  
Standard Definition ◽  
Time Symmetry ◽  
Poincaré Symmetry ◽  
Definition Of ◽  
Variational Symmetry

We argue that Poincaré symmetry can be implemented in noncommutative field theory (NCFT) if we allow the parameter of noncommutative deformation θμν to change as a two-tensor under the corresponding space–time symmetry. The implementation is consistent with the definition of θμν in terms of space–time coordinates and with the Moyal star product. Inspired by the standard definition of a variational symmetry we found a universal way to correct the implementation of the Poincaré symmetry by a term proportional to the variation of θμν in such a way that the new transformation define a symmetry of the theory. Finally we present as an example the case of NCYM theory and comment about the obstructions to implement generalized space–time symmetries in NCFT-like conformal or diffeomorphism transformations.

scholarly journals Space–time symmetry of noncommutative field theory

2005 ◽  
Vol 622 (1-2) ◽  
pp. 192-197 ◽  
Author(s):  
Cezary Gonera ◽  
Piotr Kosiński ◽  
Paweł Maślanka ◽  
Stefan Giller
Keyword(s):  
Field Theory ◽  
Space Time ◽  
Noncommutative Field Theory ◽  
Time Symmetry

Mathematical Models of Spacetime in Contemporary Physics and Essential Issues of the Ontology of Spacetime

1998 ◽  
pp. 1-5
Author(s):  
Maciej Gos
Keyword(s):  
Field Theory ◽  
Mathematical Models ◽  
Space Time ◽  
Theory Of Relativity ◽  
Time Arrow ◽  
Time Singularities ◽  
Time Quantum ◽  
Theory Of Gravitation ◽  
The Difference ◽  
Definition Of

The general theory of relativity and field theory of matter generate an interesting ontology of space-time and, generally, of nature. It is a monistic, anti-atomistic and geometrized ontology — in which the substance is the metric field — to which all physical events are reducible. Such ontology refers to the Cartesian definition of corporeality and to Plato's ontology of nature presented in the Timaeus. This ontology provides a solution to the dispute between Clark and Leibniz on the issue of the ontological independence of space-time from distribution of events. However, mathematical models of space-time in physics do not solve the problem of the difference between time and space dimensions (invariance of equations with regard to the inversion of time arrow). Recent research on space-time singularities and asymmetrical in time quantum theory of gravitation will perhaps allow for the solution of this problem based on the structure of space-time and not merely on thermodynamics.

scholarly journals Amplituhedron-like geometries

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Gabriele Dian ◽  
Paul Heslop
Keyword(s):  
Canonical Form ◽  
Star Product ◽  
Natural Extension ◽  
Tree Level ◽  
Winding Number ◽  
Alternative Definition ◽  
Standard Definition ◽  
Definition Of ◽  
Intrinsic Definition ◽  
Simple Definition

Abstract We consider amplituhedron-like geometries which are defined in a similar way to the intrinsic definition of the amplituhedron but with non-maximal winding number. We propose that for the cases with minimal number of points the canonical form of these geometries corresponds to the product of parity conjugate amplitudes at tree as well as loop level. The product of amplitudes in superspace lifts to a star product in bosonised superspace which we give a precise definition of. We give an alternative definition of amplituhedron-like geometries, analogous to the original amplituhedron definition, and also a characterisation as a sum over pairs of on-shell diagrams that we use to prove the conjecture at tree level. The union of all amplituhedron-like geometries has a very simple definition given by only physical inequalities. Although such a union does not give a positive geometry, a natural extension of the standard definition of canonical form, the globally oriented canonical form, acts on this union and gives the square of the amplitude.

scholarly journals CONFORMAL SYMMETRY OF SUPERSTRINGS ON AdS3 × S3 × T4 AND D1/D5 System

2002 ◽  
Vol 17 (37) ◽  
pp. 2477-2485 ◽  
Author(s):  
ABBAS ALI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Conformal Symmetry ◽  
Space Time ◽  
Superconformal Algebra ◽  
Superconformal Symmetry ◽  
Conformal Field ◽  
Time Symmetry

Conformal field theory of the D1/D5 system and superstrings on AdS3 × S3 × T4 is studied with particular attention to the worldsheet fields corresponding to the T4 part. A solution to the space–time N = 4 superconformal symmetry doubling and other problems is proposed. It is argued that the relevant space–time symmetry should be based on the middle N = 4 superconformal algebra. It is discussed as to why this superconformal structure has been missed so far.

THE DEFINITION OF TIME AND QUANTUM VACUUM IN 1 + 1 DIMENSIONS

1992 ◽  
Vol 07 (25) ◽  
pp. 2317-2324 ◽  
Author(s):  
A. Z. CAPRI ◽  
S. M. ROY
Keyword(s):  
Minkowski Space ◽  
Flat Space ◽  
Space Time ◽  
Quantum Vacuum ◽  
Time Translation ◽  
Minkowski Space Time ◽  
Poincaré Symmetry ◽  
Definition Of ◽  
Field Quantization ◽  
Special Space

We prove that for any (1 + 1)-dimensional globally hyperbolic space-time it is possible to define an instant of time as a special space-like geodesic which is independent of the coordinates chosen. This definition follows uniquely from the requirement of validity of Poincaré symmetry in an infinitesimal neighborhood of the hypersurface of instantaneity. The generator associated with time translation then selects the direction of time. This fact permits unambiguous field quantization of this surface. For flat space-time the corresponding time and vacuum coincide with those of Minkowski space-time. We apply these results to static and Robertson-Walker space-times.

QUANTUM FIELD THEORY ON NONCOMMUTATIVE SPACE–TIME: THE RELATION BETWEEN ULTRAVIOLET BEHAVIOUR, TOPOLOGY AND SYMMETRY

2001 ◽  
Vol 16 (04n06) ◽  
pp. 235-240
Author(s):  
M. CHAICHIAN ◽  
A. DEMICHEV ◽  
P. PREŠNAJDER
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Star Product ◽  
Space Time ◽  
Time Variable ◽  
Noncommutative Space ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Interaction Terms ◽  
Scalar Quantum

We study properties of a scalar quantum field theory on two-dimensional noncommutative space–times. We show that ultraviolet behaviour of a field theory on noncommutative spaces is sensitive to the topology of the space–time, namely to its compactness. The compactness of space-like coordinates implies discreteness of the time variable which leads to appearance of unphysical modes and violation of unitarity even in the absence of a star-product in the interaction terms. Thus, this conclusion holds also for other quantum field theories with discrete time.

Documents as Timed Abstract Objects

2012 ◽  
Author(s):  
Claus Huitfeldt ◽  
Fabio Vitali ◽  
Silvio Peroni
Keyword(s):  
Space Time ◽  
The Other ◽  
Abstract Objects ◽  
Abstract Object ◽  
Ontological Status ◽  
Standard Definition ◽  
Definition Of

At Balisage 2009 and 2010 Renear and Wickett discussed problems in reconciling the view that documents are abstract objects with the fact that they can undergo change. In this paper we present an account of documents which we believe is quite common, but which was not discussed by Renear and Wickett. According to this account documents are indeed abstract objects, but this is easily reconciled with the fact that they are created and can undergo change. We then point to a similarity between this account and the notion of so-called space-time slices. We argue that the proposed account of documents as timed abstract objects may be subject to the same kind of criticism that has been raised against the notion of space-time slices. We believe that our account fares no worse than the other accounts given of documents as abstract objects. But it still fails, and we remain agnostic about the ontological status of documents and their relation to abstract objects, as well as about the nature of abstract objects. We conclude that either documents are not (or not related to) abstract objects, or they are (or are related to) abstract objects of a kind which does not correspond to the standard definition of what an abstract object is.

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 FROM QUANTUM DEFORMATIONS OF RELATIVISTIC SYMMETRIES TO MODIFIED KINEMATICS AND DYNAMICS

2011 ◽  
Vol 20 (10) ◽  
pp. 1961-1967 ◽  
Author(s):  
JERZY LUKIERSKI
Keyword(s):  
Field Theory ◽  
Special Relativity ◽  
Minkowski Space ◽  
Star Product ◽  
Einstein Gravity ◽  
Kinematics And Dynamics ◽  
Noncommutative Field Theory ◽  
Quantum Deformations ◽  
Theory Framework

Starting from noncommutative generalization of Minkowski space we consider quantum deformed relativistic symmetries which lead to the modification of kinematics of special relativity. The noncommutative field theory framework described by means of the star product formalism is briefly described. We briefly present the quantum modifications of Einstein gravity.

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