Unitary representations of super Lie groups and applications to the classification and multiplet structure of super particles

It is well known that the category of super Lie groups (SLG) is equivalent to the category of super Harish-Chandra pairs (SHCP). Using this equivalence, we define the category of unitary representations (UR's) of a super Lie group. We give an extension of the classical inducing construction and Mackey imprimitivity theorem to this setting. We use our results to classify the irreducible unitary representations of semidirect products of super translation groups by classical Lie groups, in particular of the super Poincar\'e groups in arbitrary dimension. Finally we compare our results with those in the physical literature on the structure and classification of super multiplets.Comment: 55 pages LaTeX, some corrections added after comments by Prof. Pierre Delign

Low Latency Prefix Accumulation Driven Compound MAC Unit for Efficient FIR Filter Implementation

135–138This article presents hierarchical single compound adder-based MAC with assertion based error correction for speculation variations in the prefix addition for FIR filter design. The VLSI implementation of approximation in prefix adder results show a significant delay and complexity reductions, all this at the cost of latency measures when speculation fails during carry propagation, which is the main reason preventing the use of speculation in parallel-prefix adders in DSP applications. The speculative adder which is based on Han Carlson parallel prefix adder structure accomplishes better reduction in latency. Introducing a structured and efficient shift-add technique and explore latency reduction by incorporating approximation in addition. The improvements made in terms of reduction in latency and merits in performance by the proposed MAC unit are showed through the synthesis done by FPGA hardware. Results show that proposed method outpaces both formerly projected MAC designs using multiplication methods for attaining high speed

A quantum logical and geometrical approach to the study of improper mixtures

We study improper mixtures from a quantum logical and geometrical point of view. Taking into account the fact that improper mixtures do not admit an ignorance interpretation and must be considered as states in their own right, we do not follow the standard approach which considers improper mixtures as measures over the algebra of projections. Instead of it, we use the convex set of states in order to construct a new lattice whose atoms are all physical states: pure states and improper mixtures. This is done in order to overcome one of the problems which appear in the standard quantum logical formalism, namely, that for a subsystem of a larger system in an entangled state, the conjunction of all actual properties of the subsystem does not yield its actual state. In fact, its state is an improper mixture and cannot be represented in the von Neumann lattice as a minimal property which determines all other properties as is the case for pure states or classical systems. The new lattice also contains all propositions of the von Neumann lattice. We argue that this extension expresses in an algebraic form the fact that -alike the classical case- quantum interactions produce non trivial correlations between the systems. Finally, we study the maps which can be defined between the extended lattice of a compound system and the lattices of its subsystems.Comment: submitted to the Journal of Mathematical Physic

Inverse problems for Schrodinger equations with Yang-Mills potentials in domains with obstacles and the Aharonov-Bohm effect

We study the inverse boundary value problems for the Schr\"{o}dinger equations with Yang-Mills potentials in a bounded domain $\Omega_0\subset\R^n$ containing finite number of smooth obstacles $\Omega_j,1\leq j \leq r$. We prove that the Dirichlet-to-Neumann operator on $\partial\Omega_0$ determines the gauge equivalence class of the Yang-Mills potentials. We also prove that the metric tensor can be recovered up to a diffeomorphism that is identity on $\partial\Omega_0$.Comment: 15 page

On a certain class of semigroups of operators

We define an interesting class of semigroups of operators in Banach spaces, namely, the randomly generated semigroups. This class contains as a remarkable subclass a special type of quantum dynamical semigroups introduced by Kossakowski in the early 1970s. Each randomly generated semigroup is associated, in a natural way, with a pair formed by a representation or an antirepresentation of a locally compact group in a Banach space and by a convolution semigroup of probability measures on this group. Examples of randomly generated semigroups having important applications in physics are briefly illustrated.Comment: 11 page

A complete characterization of phase space measurements

We characterize all the phase space measurements for a non-relativistic particle.Comment: 11 pages, latex, no figures, iopart styl

Quantum gravity effects in the CGHS model of collapse to a black hole

We show that only a sector of the classical solution space of the CGHS model describes formation of black holes through collapse of matter. This sector has either right or left moving matter. We describe the sector which has left moving matter in canonical language. In the nonperturbative quantum theory all operators are expressed in terms of the matter field operator which is represented on a Fock space. We discuss existence of large quantum fluctuations of the metric operator when the matter field is approximately classical. We end with some comments which may pertain to Hawking radiation in the context of the model.Comment: Latex, 26 pages, 1 figure, to appear in Phy. Rev. D (15

Testing axioms for Quantum Mechanics on Probabilistic toy-theories

In Ref. [1] one of the authors proposed postulates for axiomatizing Quantum Mechanics as a "fair operational framework", namely regarding the theory as a set of rules that allow the experimenter to predict future events on the basis of suitable tests, having local control and low experimental complexity. In addition to causality, the following postulates have been considered: PFAITH (existence of a pure preparationally faithful state), and FAITHE (existence of a faithful effect). These postulates have exhibited an unexpected theoretical power, excluding all known nonquantum probabilistic theories. Later in Ref. [2] in addition to causality and PFAITH, postulate LDISCR (local discriminability) and PURIFY (purifiability of all states) have been considered, narrowing the probabilistic theory to something very close to Quantum Mechanics. In the present paper we test the above postulates on some nonquantum probabilistic models. The first model, "the two-box world" is an extension of the Popescu-Rohrlich model, which achieves the greatest violation of the CHSH inequality compatible with the no-signaling principle. The second model "the two-clock world" is actually a full class of models, all having a disk as convex set of states for the local system. One of them corresponds to the "the two-rebit world", namely qubits with real Hilbert space. The third model--"the spin-factor"--is a sort of n-dimensional generalization of the clock. Finally the last model is "the classical probabilistic theory". We see how each model violates some of the proposed postulates, when and how teleportation can be achieved, and we analyze other interesting connections between these postulate violations, along with deep relations between the local and the non-local structures of the probabilistic theory.Comment: Submitted to QIP Special Issue on Foundations of Quantum Informatio

Continuous slice functional calculus in quaternionic Hilbert spaces

The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest, the class of continuous functions to consider in this setting is the one of slice quaternionic functions. Slice functions generalize the concept of slice regular function, which comprises power series with quaternionic coefficients on one side and that can be seen as an effective generalization to quaternions of holomorphic functions of one complex variable. The notion of slice function allows to introduce suitable classes of real, complex and quaternionic $C^*$--algebras and to define, on each of these $C^*$--algebras, a functional calculus for quaternionic normal operators. In particular, we establish several versions of the spectral map theorem. Some of the results are proved also for unbounded operators. However, the mentioned continuous functional calculi are defined only for bounded normal operators. Some comments on the physical significance of our work are included.Comment: 71 pages, some references added. Accepted for publication in Reviews in Mathematical Physic