scholarly journals Bulk reconstruction and Bogoliubov transformations in AdS2

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Parijat Dey ◽  
Nirmalya Kajuri
Keyword(s):  
Conformal Transformations ◽  
Bogoliubov Transformation ◽  
Massless Particles ◽  
Creation And Annihilation Operators ◽  
Global Modes ◽  
Boundary Representations ◽  
Bogoliubov Transformations ◽  
Massless Fields

Abstract In the bulk reconstruction program, one constructs boundary representations of bulk fields. We investigate the relation between the global/Poincare and AdS-Rindler representations for AdS2. We obtain the AdS-Rindler smearing function for massive and massless fields and show that the global and AdS-Rindler boundary representations are related by conformal transformations. We also use the boundary representations of creation and annihilation operators to compute the Bogoliubov transformation relating global modes to AdS-Rindler modes for both massive and massless particles.

scholarly journals Singular Bogoliubov transformations and inequivalent representations of canonical commutation relations

2019 ◽  
Vol 31 (08) ◽  
pp. 1950026 ◽  
Author(s):  
Asao Arai
Keyword(s):  
Fock Space ◽  
Sufficient Conditions ◽  
Bogoliubov Transformation ◽  
Fock Representation ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Direct Sum ◽  
Boson Fock Space ◽  
Inequivalent Representations ◽  
Bogoliubov Transformations

We introduce a concept of singular Bogoliubov transformation on the abstract boson Fock space and construct a representation of canonical commutation relations (CCRs) which is inequivalent to any direct sum of the Fock representation. Sufficient conditions for the representation to be irreducible are formulated. Moreover, an example of such representations of CCRs is given.

Fermionic Formulation of the Ising Model

2020 ◽  
pp. 319-340
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Ising Model ◽  
Dirac Equation ◽  
Quadratic Form ◽  
Continuum Limit ◽  
Majorana Fermions ◽  
Bogoliubov Transformation ◽  
Crucial Aspect ◽  
Creation And Annihilation Operators ◽  
Order And Disorder ◽  
The Continuum

A crucial aspect of the Ising model is its fermionic nature and this chapter is devoted to this property of the model. In the continuum limit, a Dirac equation for neutral Majorana fermions emerges. The details of the derivation are much less important than understanding why it is possible. The chapter emphasizes the simplicity and the exactness of the result, and covers the so-called Wigner-Jordan transformation, which brings the original Hamiltonian to a quadratic form in the creation and annihilation operators of the fermions. It covers the role played by the Bogoliubov transformation and the importance of the order and disorder operators.

Tensor Product Decomposition, Entanglement, and Bogoliubov Transformations for Two Fermion System

2005 ◽  
Vol 12 (02) ◽  
pp. 179-188 ◽  
Author(s):  
Paweł Caban ◽  
Krzysztof Podlaski ◽  
Jakub Rembieliński ◽  
Kordian A. Smoliński ◽  
Zbigniew Walczak
Keyword(s):  
Hilbert Space ◽  
Tensor Product ◽  
Explicit Formula ◽  
Fermion System ◽  
Density Matrices ◽  
Product Decomposition ◽  
Creation And Annihilation Operators ◽  
Separable States ◽  
Entanglement Of Formation ◽  
Bogoliubov Transformations

We consider the two-fermion system whose states are subjected to the superselection rule forbidding the superposition of states with fermionic and bosonic statistics. This implies that separable states are described only by diagonal density matrices. Moreover, we find the explicit formula for the entanglement of formation, which in this case cannot be calculated properly using Wootters's concurrence. We also discuss the problem of the choice of tensor product decomposition in a system of two fermions with the help of Bogoliubov transformations of creation and annihilation operators. Finally, we show that there exist states which are separable with respect to all tensor product decompositions of the underlying Hilbert space.

scholarly journals KALB–RAMOND FIELDS IN THE PETIAU–DUFFIN–KEMMER FORMALISM AND SCALE INVARIANCE

2010 ◽  
Vol 25 (32) ◽  
pp. 2745-2751 ◽  
Author(s):  
S. I. KRUGLOV
Keyword(s):  
Wave Equation ◽  
Density Matrix ◽  
Scale Invariance ◽  
Conformal Symmetry ◽  
Relativistic Wave Equation ◽  
Relativistic Wave ◽  
Massless Particles ◽  
First Order ◽  
Dilatation Current ◽  
Massless Fields

Kalb–Ramond equations for massive and massless particles are considered in the framework of the Petiau–Duffin–Kemmer formalism. We obtain 10×10 matrices of the relativistic wave equation of the first-order and solutions in the form of density matrix. The canonical and Belinfante energy–momentum tensors are found. We investigate the scale invariance and obtain the conserved dilatation current. It was demonstrated that the conformal symmetry is broken even for massless fields.

scholarly journals From pseudo-bosons to pseudo-Hermiticity via multiple generalized Bogoliubov transformations

2017 ◽  
Vol 31 (12) ◽  
pp. 1750085 ◽  
Author(s):  
Fabio Bagarello ◽  
Andreas Fring
Keyword(s):  
Simple Model ◽  
Model Parameters ◽  
Bogoliubov Transformation ◽  
System A ◽  
Different Types ◽  
The One ◽  
Bogoliubov Transformations

We consider the special type of pseudo-bosonic systems that can be mapped to standard bosons by means of generalized Bogoliubov transformation and demonstrate that pseudo-Hermitian systems can be obtained from them by means of a second subsequent Bogoliubov transformation. We employ these operators in a simple model and study three different types of scenario for the constraints on the model parameters giving rise to a Hermitian system, a pseudo-Hermitian system in which the second Bogoliubov transformation is equivalent to the associated Dyson map and the one in which we obtain [Formula: see text]-quasi bases.

Discussion following the presentation by F. Deubner

1977 ◽  
Vol 36 ◽  
pp. 69-74
Keyword(s):  
List Type ◽  
The Sun ◽  
Type Number ◽  
Harmonic Motion ◽  
Locally Excited ◽  
Long Period ◽  
Coherent Wave ◽  
Short Period ◽  
Global Modes

The discussion was separated into 3 different topics according to the separation made by the reviewer between the different periods of waves observed in the sun :1) global modes (long period oscillations) with predominantly radial harmonic motion.2) modes with large coherent - wave systems but not necessarily global excitation (300 s oscillation).3) locally excited - short period waves.

Energy and Momentum

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Time Dilation ◽  
Speed Of Light ◽  
Massless Particles ◽  
The Everyday ◽  
Low Speeds ◽  
Energy And Momentum ◽  
Deep Relationship ◽  
Insight Into ◽  
Momentum Relation

Tis chapter explains the famous equation E = mc2 as part of a wider relationship between energy, mass, and momentum. We start by defning energy and momentum in the everyday sense. We then build on the stretching‐triangle picture of spacetime vectors developed in Chapter 11 to see how energy, mass, and momentum have a deep relationship that is not obvious at everyday low speeds. When momentum is zero (a mass is at rest) this energy‐momentum relation simplifes to E = mc2, which implies that mass at rest quietly stores tremendous amounts of energy. Te energymomentum relation also implies that traveling near the speed of light (e.g., to take advantage of time dilation for interstellar journeys) will require tremendous amounts of energy. Finally, we look at the simplifed form of the energy‐momentum relation when the mass is zero. Tis gives us insight into the behavior of massless particles such as the photon.

scholarly journals Free fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Marius de Leeuw ◽  
Chiara Paletta ◽  
Anton Pribytok ◽  
Ana L. Retore ◽  
Alessandro Torrielli
Keyword(s):  
Spectral Problem ◽  
Transfer Matrix ◽  
Arbitrary Number ◽  
Free Fermion ◽  
Nearest Neighbour ◽  
Bogoliubov Transformation ◽  
Free Fermions ◽  
New Models ◽  
Lower Dimensional

Abstract In this paper we first demonstrate explicitly that the new models of integrable nearest-neighbour Hamiltonians recently introduced in PRL 125 (2020) 031604 [36] satisfy the so-called free fermion condition. This both implies that all these models are amenable to reformulations as free fermion theories, and establishes the universality of this condition. We explicitly recast the transfer matrix in free fermion form for arbitrary number of sites in the 6-vertex sector, and on two sites in the 8-vertex sector, using a Bogoliubov transformation. We then put this observation to use in lower-dimensional instances of AdS/CFT integrable R-matrices, specifically pure Ramond-Ramond massless and massive AdS3, mixed-flux relativistic AdS3 and massless AdS2. We also attack the class of models akin to AdS5 with our free fermion machinery. In all cases we use the free fermion realisation to greatly simplify and reinterpret a wealth of known results, and to provide a very suggestive reformulation of the spectral problem in all these situations.

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