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.

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 How Does Spacetime “Tell an Electron How to Move”?

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2283
Author(s):  
Garnet Ord
Keyword(s):  
Special Relativity ◽  
Minkowski Space ◽  
Continuum Limit ◽  
Minkowski Spacetime ◽  
Discrete Space ◽  
Kinematics And Dynamics ◽  
Uniform Motion ◽  
Classical Particles

Minkowski spacetime provides a background framework for the kinematics and dynamics of classical particles. How the framework implements the motion of matter is not specified within special relativity. In this paper we specify how Minkowski space can implement motion in such a way that ’quantum’ propagation occurs on appropriate scales. This is done by starting in a discrete space and explicitly taking a continuum limit. The argument is direct and illuminates the special tension between ’rest’ and ’uniform motion’ found in Minkowski space, showing how the formal analytic continuations involved in Minkowski space and quantum propagation arise from the same source.

scholarly journals κ-DEFORMED SNYDER SPACETIME

2010 ◽  
Vol 25 (08) ◽  
pp. 579-590 ◽  
Author(s):  
S. MELJANAC ◽  
D. MELJANAC ◽  
A. SAMSAROV ◽  
M. STOJIĆ
Keyword(s):  
Special Relativity ◽  
Minkowski Space ◽  
Star Product ◽  
Leibniz Rule ◽  
New Class ◽  
Special Cases ◽  
Poincaré Algebra

We present Lie-algebraic deformations of Minkowski space with undeformed Poincaré algebra. These deformations interpolate between Snyder and κ-Minkowski space. We find realizations of noncommutative coordinates in terms of commutative coordinates and derivatives. Deformed Leibniz rule, the coproduct structure and star product are found. Special cases, particularly Snyder and κ-Minkowski in Maggiore-type realizations are discussed. Our construction leads to a new class of deformed special relativity theories.

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 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 Chern-Simons gravity dual of BCFT

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Tadashi Takayanagi ◽  
Takahiro Uetoko
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Entanglement Entropy ◽  
Einstein Gravity ◽  
Conformal Field ◽  
Holographic Entanglement Entropy ◽  
The World ◽  
Higher Spin ◽  
End Of The World ◽  
Chern Simons

Abstract In this paper we provide a Chern-Simons gravity dual of a two dimensional conformal field theory on a manifold with boundaries, so called boundary conformal field theory (BCFT). We determine the correct boundary action on the end of the world brane in the Chern-Simons gauge theory. This reproduces known results of the AdS/BCFT for the Einstein gravity. We also give a prescription of calculating holographic entanglement entropy by employing Wilson lines which extend from the AdS boundary to the end of the world brane. We also discuss a higher spin extension of our formulation.

scholarly journals LOCALITY, CAUSALITY AND NONCOMMUTATIVE GEOMETRY

2006 ◽  
Vol 21 (01) ◽  
pp. 67-82 ◽  
Author(s):  
CHONG-SUN CHU ◽  
KO FURUTA ◽  
TAKEO INAMI
Keyword(s):  
Field Theory ◽  
Noncommutative Geometry ◽  
Light Cone ◽  
Energy Condition ◽  
Noncommutative Space ◽  
Noncommutative Field Theory ◽  
Causality Condition ◽  
Usual Form ◽  
New Form ◽  
Lower Dimensional

We analyze the causality condition in noncommutative field theory and show that the nonlocality of noncommutative interaction leads to a modification of the light cone to the light wedge. This effect is generic for noncommutative geometry. We also check that the usual form of energy condition is violated and propose that a new form is needed in noncommutative space–time. On reduction from light cone to light wedge, it looks like the noncommutative dimensions are effectively washed out and suggests a reformulation of noncommutative field theory in terms of lower dimensional degree of freedom. This reduction of dimensions due to noncommutative geometry could play a key role in explaining the holographic property of quantum gravity.

scholarly journals Noncommutative Field Theory and Lorentz Violation

2001 ◽  
Vol 87 (14) ◽  
Author(s):  
Sean M. Carroll ◽  
Jeffrey A. Harvey ◽  
V. Alan Kostelecký ◽  
Charles D. Lane ◽  
Takemi Okamoto
Keyword(s):  
Field Theory ◽  
Lorentz Violation ◽  
Noncommutative Field Theory

scholarly journals Hermitian realizations of κ-Minkowski space–time

2015 ◽  
Vol 30 (03) ◽  
pp. 1550019 ◽  
Author(s):  
Domagoj Kovačević ◽  
Stjepan Meljanac ◽  
Andjelo Samsarov ◽  
Zoran Škoda
Keyword(s):  
Minkowski Space ◽  
Star Product ◽  
Plane Waves ◽  
Space Time ◽  
Star Products ◽  
Systematic Construction ◽  
Minkowski Space Time ◽  
Noncommutative Plane

General realizations, star products and plane waves for κ-Minkowski space–time are considered. Systematic construction of general Hermitian realization is presented, with special emphasis on noncommutative plane waves and Hermitian star product. Few examples are elaborated and possible physical applications are mentioned.

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