On the Gelfand–Dickey algebra GD(SLn) and the Wn‐symmetry. I. The bosonic case

1994 ◽  
Vol 35 (6) ◽  
pp. 3190-3210 ◽  
Author(s):  
E. H. Saidi ◽  
M. B. Sedra
Keyword(s):  
Bosonic Case

Quantum entanglement of Dirac field in background of an asymptotically flat static black hole

2010 ◽  
Vol 10 (11&12) ◽  
pp. 947-955
Author(s):  
Jieci Wang ◽  
Qiyuan Pan ◽  
Songbai Chen ◽  
Jiliang Jing
Keyword(s):  
Black Hole ◽  
Mutual Information ◽  
Quantum Entanglement ◽  
Hawking Temperature ◽  
Universal Property ◽  
Dirac Field ◽  
Initial Value ◽  
Asymptotically Flat ◽  
Static Black Hole ◽  
Bosonic Case

The entanglement of the Dirac field in the asymptotically flat black hole is investigated. Unlike the bosonic case in which the initial entanglement vanishes in the limit of infinite Hawking temperature, in this case the entanglement achieves a nonvanishing minimum values, which shows that the entanglement is never completely destroyed when black hole evaporates completely. Another interesting result is that the mutual information in this limit equals to just half of its own initial value, which may be an universal property for any fields.

Parafermion theory from the q-deformed algebra with q a root of unity

2020 ◽  
Vol 17 (03) ◽  
pp. 2050045
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Partition Function ◽  
Specific Heat ◽  
Set Theory ◽  
Fock Space ◽  
Infinite Dimensional ◽  
Root Of Unity ◽  
Deformed Algebra ◽  
Bosonic Case ◽  
Fermionic Case ◽  
Bosonic Limit

In this paper, we find the [Formula: see text]-deformed algebra with the finite- and infinite-dimensional Fock space and both the fermionic limit and the bosonic limit. Using the cardinality of set theory, we propose the Hamiltonian interpolating bosonic case and fermionic case, which enables us to construct the proper partition function and internal energy. As examples, we discuss the specific heat of free [Formula: see text] parafermion gas model and [Formula: see text] parafermion star.

scholarly journals STABILITY FOR A SYSTEM OF N FERMIONS PLUS A DIFFERENT PARTICLE WITH ZERO-RANGE INTERACTIONS

2012 ◽  
Vol 24 (07) ◽  
pp. 1250017 ◽  
Author(s):  
M. CORREGGI ◽  
G. DELL'ANTONIO ◽  
D. FINCO ◽  
A. MICHELANGELI ◽  
A. TETA
Keyword(s):  
Quantum System ◽  
Stability Problem ◽  
Relativistic Quantum ◽  
The Other ◽  
Range Interaction ◽  
Symmetric Extension ◽  
A Value ◽  
Zero Range ◽  
Bosonic Case ◽  
The Stability

We study the stability problem for a non-relativistic quantum system in dimension three composed by N ≥ 2 identical fermions, with unit mass, interacting with a different particle, with mass m, via a zero-range interaction of strength α ∈ ℝ. We construct the corresponding renormalized quadratic (or energy) form [Formula: see text] and the so-called Skornyakov–Ter–Martirosyan symmetric extension Hα, which is the natural candidate as Hamiltonian of the system. We find a value of the mass m*(N) such that for m > m*(N) the form [Formula: see text] is closed and bounded from below. As a consequence, [Formula: see text] defines a unique self-adjoint and bounded from below extension of Hα and therefore the system is stable. On the other hand, we also show that the form [Formula: see text] is unbounded from below for m < m*(2). In analogy with the well-known bosonic case, this suggests that the system is unstable for m < m*(2) and the so-called Thomas effect occurs.

SUPER-LIOUVILLE THEORY AS A TWO-DIMENSIONAL, SUPERCONFORMAL SUPERGRAVITY THEORY

1990 ◽  
Vol 05 (02) ◽  
pp. 391-414 ◽  
Author(s):  
JACQUES DISTLER ◽  
ZVONIMIR HLOUSEK ◽  
HIKARU KAWAI
Keyword(s):  
String Theory ◽  
Hausdorff Dimension ◽  
Critical Exponents ◽  
Liouville Theory ◽  
Two Dimensional ◽  
Random Surfaces ◽  
Supergravity Theory ◽  
Arbitrary Topology ◽  
Bosonic Case

In this paper we extend our previous results on the bosonic Liouville theory, to the supersymmetric case. As in the bosonic case, we find that the quantization of the N=1 theory is limited to the region D≤1. We compute the exact critical exponents and the analogue of the Hausdorff dimension of super random surfaces. Our procedure is manifestly covariant and our results hold for the surface of arbitrary topology. We also examine the N=2, O(2) string theory and find that it appears to be well-defined for all D.

scholarly journals CORRELATION FUNCTIONS OF MINIMAL MODELS COUPLED TO TWO-DIMENSIONAL QUANTUM SUPERGRAVITY

1992 ◽  
Vol 07 (04) ◽  
pp. 333-343 ◽  
Author(s):  
KENICHIRO AOKI ◽  
ERIC D’HOKER
Keyword(s):  
Correlation Functions ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Minimal Models ◽  
Point Correlation ◽  
Bosonic Case

We compute the three-point functions of Neveu-Schwarz primary fields of the minimal models on the sphere when coupled to supergravity in two dimensions. The results show that the three-point correlation functions are determined by the scaling dimensions of the fields, as in the bosonic case.

scholarly journals Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shock waves

2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Maxim Olshanii ◽  
Dumesle Deshommes ◽  
Jordi Torrents ◽  
Marina Gonchenko ◽  
Vanja Dunjko ◽  
...  
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Initial Conditions ◽  
Broad Class ◽  
Hydrodynamic Equations ◽  
Nonlinear Transport ◽  
One Dimensional ◽  
Nonlinear Transport Equation ◽  
Bosonic Case ◽  
The One

The recently proposed map [5] between the hydrodynamic equations governing the two-dimensional triangular cold-bosonic breathers [1] and the high-density zero-temperature triangular free-fermionic clouds, both trapped harmonically, perfectly explains the former phenomenon but leaves uninterpreted the nature of the initial (t=0) singularity. This singularity is a density discontinuity that leads, in the bosonic case, to an infinite force at the cloud edge. The map itself becomes invalid at times t<0t<0. A similar singularity appears at t = T/4t=T/4, where T is the period of the harmonic trap, with the Fermi-Bose map becoming invalid at t > T/4t>T/4. Here, we first map—using the scale invariance of the problem—the trapped motion to an untrapped one. Then we show that in the new representation, the solution [5] becomes, along a ray in the direction normal to one of the three edges of the initial cloud, a freely propagating one-dimensional shock wave of a class proposed by Damski in [7]. There, for a broad class of initial conditions, the one-dimensional hydrodynamic equations can be mapped to the inviscid Burgers’ equation, which is equivalent to a nonlinear transport equation. More specifically, under the Damski map, the t=0 singularity of the original problem becomes, verbatim, the initial condition for the wave catastrophe solution found by Chandrasekhar in 1943 [9]. At t=T/8t=T/8, our interpretation ceases to exist: at this instance, all three effectively one-dimensional shock waves emanating from each of the three sides of the initial triangle collide at the origin, and the 2D-1D correspondence between the solution of [5] and the Damski-Chandrasekhar shock wave becomes invalid.

scholarly journals N = 1, 2 SUPER-NLS HIERARCHIES AS SUPER-KP COSET REDUCTIONS

1995 ◽  
Vol 10 (06) ◽  
pp. 895-922 ◽  
Author(s):  
F. TOPPAN
Keyword(s):  
Covariant Derivative ◽  
Equations Of Motion ◽  
Free Field ◽  
Algebra Structure ◽  
Kp Hierarchy ◽  
Nls Equation ◽  
Bosonic Case ◽  
Free Fields

We define consistent finite-superfield reductions of the N = 1, 2 super-KP hierarchies via the coset approach we have already developed for reducing the bosonic KP hierarchy [generating for example the NLS hierarchy from the [Formula: see text] coset]. We work in a manifestly supersymmetric framework and illustrate our method by treating explicitly the N = 1, 2 super-NLS hierarchies. With respect to the bosonic case the ordinary covariant derivative is now replaced by a spinorial one which contains a spin-[Formula: see text] superfield. Each coset reduction is associated with a rational super-[Formula: see text] algebra encoding a nonlinear super-[Formula: see text]-algebra structure. In the N = 2 case two conjugate sets of super-Lax operators, equations of motion and infinite Hamiltonians in involution are derived. Modified hierarchies are obtained from the original ones via free-field mappings [just as an m-NLS equation arises from representing the [Formula: see text] algebra through the classical Wakimoto free fields].

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