Connection between space-time supersymmetry and non-commutative geometry

Connection between Space-Time Supersymmetry and Non-Commutative Geometry

The non-commutative geometric construction of A. Connes [1-5] has been successful in giving a geometrical interpretation of the standard model as well as some grand unification models. Our lack of ability to quantize the non-commutative actions forced on us to quantize the classical actions resulting from the non-commutative ones by adopting the usual rules. The symmetries that might be present...

Non–Commutative Geometry on Quantum Phase–Space

A non–commutative analogue of the classical differential forms is constructed on the phase–space of an arbitrary quantum system. The non– commutative forms are universal and are related to the quantum mechanical dynamics in the same way as the classical forms are related to classical dynamics. They are constructed by applying the Weyl–Wigner symbol map to the differential envelope of the linear...

Eth - Th / 93 - 24 Some Elements of Connes ’ Non - Commutative Geometry , and Space - Time Geometry

Covariantly Quantized Spinning Particle and Its Possible Connection to Non-commutative Space-time

Covariant quantization of the Nambu-Goto spinning particle in 2+1-dimensions is studied. The model is relevant in the context of recent activities in non-commutative space-time. From a technical point of view also covariant quantization of the model poses an interesting problem: the set of second class constraints (in the Dirac classification scheme) is reducible. The reducibility problem is an...

Inflation on a non-commutative space–time

Article history: Received 24 April 2015 Received in revised form 9 June 2015 Accepted 11 June 2015 Available online 16 June 2015 Editor: M. Trodden We study inflation on a non-commutative space–time within the framework of enveloping algebra approach which allows for a consistent formulation of general relativity and of the standard model of particle physics. We show that within this framework,...