X iv :q ua nt -p h/ 03 05 15 0v 1 2 4 M ay 2 00 3 Particle and Field Symmetries and Noncommutative Geometry Ajay Patwardhan Physics Department, St.Xavier’s College, Mahapalika Marg, Mumbai 400001, India. * e-mail : [email protected] Abstract The development of Noncommutative geometry is creating a reworking and new possibilities in physics. This paper identifies some of the commutation and d...

Following the introduction of the invariant distance on the non-commutative C-algebra of the quantum group SUq(2), the Green function and the Kernel on the q-homogeneous space M = SU(2)q/U(1) are derived. A path integration is formulated. Green function for the free massive scalar field on the non-commutative Einstein space R ×M is presented.

We extend the concept of implementability of semigroups of evolution operators associated with dynamical systems to quantum case. We show that such an extension can be properly formulated in terms of Jordan morphisms and isometries on non-commutative L p spaces. We focus our attention on a non-commutative analog of the Banach-Lamperti theorem.

Quantum mechanics of composite systems, gives rise to certain special states called entangled states. A physical system, that is in an entangled state displays an intricate correlation between its subsystems. There are also some composite quantum states (classically correlated states or separable states) that are not entangled. It is generally claimed, often without a rigorous proof to support,...

We numerically solve the functional differential equations (FDE’s) of 2-particle electrodynamics, using the full electrodynamic force obtained from the retarded Lienard-Wiechert potentials and the Lorentz force law. In contrast, the usual formulation uses only the Coulomb force (scalar potential), reducing the electrodynamic 2-body problem to a system of ordinary differential equations (ODE’s)....

We construct a rigourous model of quantum measurement. A two-state model of a negative temperature amplifier, such as a laser, is taken to a classical thermodynamic limit. In the limit, it becomes a classical measurement apparatus obeying the stochastic axioms of quantum mechanics. Thus we derive the probabilities from a deterministic Schroedinger's equation by procedures analogous to those of ...

Elliptic Quantum Planes means here non-commutative deformations of the complex projective plane P(C). We consider deformations in the realm of non-commutative (complex) algebraic geometry. As we recall in the first section, elliptic modulus parameter enters into the game. Hence the adjective “elliptic” is used. Note also that, in that world, the complex projective line P(C), namely the Riemann ...

In a recent paper Bernevig, Brodie, Susskind and Toumbas constructed a brane realization of the Quantum Hall fluid. Since then it has been realized that the Quantum Hall system is very closely related to non–commutative Chern Simons theory and this suggests alternative brane constructions which we believe are more reliable and clear. In this paper a brane construction is given for the non–commu...

Alice and Bob receive a bipartite state (possibly entangled) from some finite collection or from some subspace. Alice sends a message to Bob through a noisy quantum channel such that Bob may determine the initial state, with zero chance of error. This framework encompasses, for example, teleportation, dense coding, entanglement assisted quantum channel capacity, and one-way communication comple...

We are studying the dynamics of a one-dimensional field in a noncommutative Euclidean space. The non-commutative space we consider is the one that emerges in the context of three dimensional Euclidean quantum gravity: it is a deformation of the classical Euclidean space E3 and the Planck length lP plays the role of the deformation parameter. The field is interpreted as a particle which evolves ...