Quantum Fields on the Groenewold - Moyal Plane 1
نویسندگان
چکیده
We give an introductory review of quantum physics on the noncommutative space-time called the Groenewold-Moyal plane. Basic ideas like star products, twisted statistics , second quantized fields and discrete symmetries are discussed. We also outline some of the recent developments in these fields and mention where one can search for experimental signals.
منابع مشابه
Causality and Statistics on the Groenewold - Moyal Plane
Quantum theories constructed on the noncommutative spacetime called the Groenewold-Moyal plane exhibit many interesting properties such as Lorentz and CPT noninvariance, causality violation and twisted statistics. We show that such violations lead to many striking features that may be tested experimentally. These theories predict Pauli forbidden transitions due to twisted statistics, anisotropi...
متن کاملThe ⋆-value Equation and Wigner Distributions in Noncommutative Heisenberg algebras∗
We consider the quantum mechanical equivalence of the Seiberg-Witten map in the context of the Weyl-Wigner-Groenewold-Moyal phase-space formalism in order to construct a quantum mechanics over noncommutative Heisenberg algebras. The formalism is then applied to the exactly soluble Landau and harmonic oscillator problems in the 2-dimensional noncommutative phase-space plane, in order to derive t...
متن کاملTwisted Poincaré Invariant Quantum Field Theories
It is by now well known that the Poincaré group acts on the Moyal plane with a twisted coproduct. Poincaré invariant classical field theories can be formulated for this twisted coproduct. In this paper we systematically study such a twisted Poincaré action in quantum theories on the Moyal plane. We develop quantum field theories invariant under the twisted action from the representations of the...
متن کاملA selection principle in deformation quantization
Deformation quantization produces families of mathematically equivalent quantization procedures from which one must select the physically meaningful ones. As a selection principle we propose that the procedure must allow enough ‘observable’ energy distributions, i.e., ones for which no pure quantum state will appear with negative probability and must further have the property that for these the...
متن کاملAnticommutators and propagators of Moyal star-products for Dirac field on noncommutative spacetime
We study the Moyal anticommutators and their expectation values between vacuum states and non-vacuum states for Dirac fields on noncommutative spacetime. Then we construct the propagators of Moyal star-products for Dirac fields on noncommutative spacetime. We find that the propagators of Moyal star-products for Dirac fields are equal to the propagators of Dirac fields on ordinary commutative sp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008