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arXiv:1512.03716

Fermionic quantum operations: a computational framework II. Examples, monoaxiality, scalings

Gyula Lakos

Published Nov 27, 2015• 0 citations
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Abstract

The objective of this series of papers is to recover information regarding the behaviour of FQ operations in the case $n=2$, and FQ conform-operations in the case $n=3$. In this second part we show some arithmetically constructible examples of FQ operations ($n=2$), concentrating on monoaxiality, related extensions, and (hyper)scaling.

DOI
10.48550/arxiv.1512.03716

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The objective of this series of papers is to recover information regarding the behaviour of FQ operations in the case n=2n=2n=2, and FQ conform-operations in the case n=3n=3n=3. In this second part we show some arithmetically constructible examples of FQ operations (n=2n=2n=2), concentrating on monoaxiality, related extensions, and (hyper)scaling.
The objective of this series of papers is to recover information regarding the behaviour of FQ operations in the case n=2n=2n=2, and FQ conform-operations in the case n=3n=3n=3. In this first part we study how the basic invariance properties of FQ operations (n=2n=2n=2) are reflected in their formal power series expansions.
We study twist operators in higher dimensional CFT’s. In particular, we express their conformal dimension in terms of the energy density for the CFT in a particular thermal ensemble. We construct an expansion of the conformal dimension in power series around n =1, with n being replica parameter. We show that the coefficients in this expansion are determined by higher point correlations of the energy-momentum tensor. In particular, the first and second terms, i.e. the first and second derivatives of the scaling dimension, have a simple universal form. We test these results using holography and free field theory computations, finding agreement in both cases. We also consider the ‘operator product expansion’ of spherical twist operators and finally, we examine the behaviour of correlators of twist operators with other operators in the limit n → 1.
In a recent series of papers, we have analyzed a certain deformation of the canonical commutation relations producing an interesting functional structure which has been proved to have some connections with physics, and in particular with quasi-Hermitian quantum mechanics. Here we repeat a similar analysis starting with the canonical anticommutation relations. We will show that in this case, most of the assumptions needed in the former situation are automatically satisfied, making our construction rather friendly . We discuss some examples of our construction, again related to quasi-Hermitian quantum mechanics, and the bi-coherent states for the system. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.