# Boson Mappings Of The Fermion Dynamical Symmetry Model

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### Numerical Renormalization-Group Study of the Bose-Fermi Kondo

connection with heavy-fermion criticality. For 0

### REPORT DOCUMENTATION PAGE Form Approved

We first constructed a sequence of theoretical steps connecting the classical O(2) model in 1+1 dimensions to a boson model that can be implemented on optical lattices, showing a proof-of-principle that quantum computing via 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND SUBTITLE 13. SUPPLEMENTARY NOTES 12. DISTRIBUTION AVAILIBILITY STATEMENT 6

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May 15, 2019 Abraham-Shrauner B: Lie symmetry solutions for anomalous diffusion 2547 Abreu L D: Sampling theory associated with q-difference equations of the Sturm Liouville type 10311 Abreu L M and de Montigny M: Galilean covariant models of bosons coupled to a Chern Simons gauge ﬁeld 9877 Ackad E and Horbatsch M: Numerical solution of

### COLLECTIVE MOTION IN DEFORMED EVEN-EVEN ACTINIDE NUCLEI

microscopic foundation of the Fermion Dynamical Symmetry Model because the model is based on the collective SD-pairs. The pair approximation is found to be useful, therefore we use it as an optimum approximation to the full shell-model as the size of the pair space is much smaller than that of the full space.

### Boson-fermion mapping and dynamical supersymmetry in fermion

recent fermion dynamical symmetry model (FDSM) analysis [13]. Our formalism is thus tailor made to investigate the similarities and di erences between the two approaches. III. DYSON BOSON-FERMION MAPPING OF THE COLLECTIVE ALGEBRA In order to keep the paper as self-contained as possible, we brieﬂy retrace the basic = ˜ ]. The + +

### Introduction-Blois.2011.May12 - viXra.org

Dynamical systems modeling could be employed right after evolution through the quantum dot regime. The diagram, would look like an application of the Gauss mapping of [11].[12] [ α ] β ~ ~ exp 2 xi+1 = − ⋅xi + (24) Now that we have a model as to a change in space time geometry, let us consider what happen during the

### Symmetry and Duality in Bosonization of Two-Dimensional Dirac

Recent work on a family of boson-fermion mappings has emphasized the interplay of symmetry and duality: Phases related by a particle-vortex duality of bosons (fermions) are related by time-reversal symmetry in their fermionic (bosonic) formulation. We present exact mappings for a number of concrete

### Symmetry Conserving Dynamical Mappings - CERN

approach using the very concept of dynamical mappings. As an example, consider the toy model of QFT, the 4-theory with a continuous O(N+1) symmetry. The lagrangian density with the appropriate scaling reads L = 1 2 h (@ ~ˇ) 2 +(@ ˙) 2 i − 2 2 h ~ˇ2+˙2 i − 4N h ~ˇ2+˙2 i2 + p Nc˙; (1) where ~ˇ(x) stands for a N-componentspion eldand

### Is Nature fundamentally continuous or discrete, and how can

bang. Our second consideration is, that symmetry breaking models, i.e. the Higgs boson are not necessary for the formation of particles with mass just before Octonionic gravity which could arise in pre Planckian physics models without a potential. Finally, the necessity of potentials for pre Octonionic gravity physics

### Order of Time Derivatives in Quantum-Mechanical Equations

idea of Poincare symmetry. But, after the fall of the primary substantial interpretation by Schrödinger, it was compatible with the Born statistical interpretation of his formalism, and with the corresponding continuity equation for the probabilistic density (Veltman, 2003). Later on history was rather complicated.

### List of publications

9. A uni cation of boson expansion theories. (II) Boson expansions as provided by the functional representation method : J. Dobaczewski, Nucl. Phys. A369 (1981) 237

### Analytical solutions for the LMG model

<0 is the fermion vacuum state, and. J is given by 3 It is obvious that the Hamiltonian in this case has y SU 2 >SO 2 dynamical symmetry. Hence, the eigenvalue problem can be exactly solved in an SU 2 >SO 2 adapted basis. Case 2. V/0 and W 22)V In this case, the SU 2 >SO 2 basis vectors are no longer the eigenstates of the

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May 16, 2019 the interacting boson model (IBM) 131 and interacting boson fermion model (IBFM) [4] by fermion pairs introduced in the shell model (SM) and in the fermion dynamical symmetry model (FDSM) [5], referred to here as the interacting fermion model (IFM). Recently the possibility of obtaining analogues of the Dyson mapping for boson pairs [6-81, for

### First-principlesquantumdynamicsforfermions:Application

In this work we perform ﬁrst-principles dynamical simu-lations of a fermion-boson model. We use a Gaussian stochastic method based on a generalized phase-space representation of the quantum density operator [13]. The fermion-boson model forms the underlying basis for a broad range of phenomena in condensed-matter and ultra-cold atom physics.

### arXiv:nucl-th/9606043v1 20 Jun 1996

Apart from providing a concrete link between fermion dynamics and dynamical super-symmetry, the use of boson-fermion mappings also allows one to construct various transition operators appropriate to the boson-fermion description. This is in contrast to the phe-

### QUANTUM ALGEBRAIC DESCRIPTION OF THE PAIRING CORRELATIONS IN

nuclear collective motion, such as the Interacting Boson Model (IBM) ([21], see [22,23] for recent overviews) and the shell model. Since q-bosons also satisfy commutation relations different from the usual ones, it is reasonable to check to what extend correlated fermion pairs can be described in terms of q-deformed bosons.

### arXiv:nucl-th/0211081v1 26 Nov 2002

boson-fermion mappings which show that dynamical supersymmetry can arise in a fermion system without violation of the Pauli principle. Dynamicalsupersymmetryon the phenomenological level concerns situ-ations where states of a quantum system with even and odd fermion num-bers can be uniﬁed in a single representation of a certain supergroup. In the

### INCLUSIVE SPECTRA OF REACTIONS Fe(P,XP), (P,Xa) MEASURED AT E

dynamical symmetries. In the present work we investigate boson mappings relevant to the fermionic dynamical symmetry model. The proton-neutron dynamical symmetry model situation of no broken pairs and no scattering of pairs between normal and abnormal parity levels is considered, but we do not restrict the analysis to dynamical symmetry limits

### OF FREEDOM IN A PARTIAL RANDOM PHASE APPROXIMATION

symmetry state. In the broken symmetry state, the model nucleus assumes a deformed equilibrium shape. On the other hand, if one admits an intrinsic structure as, for example, in the U(3)-boson model 17) (the hydrodynamic limit of the microscopic

### Consistent baryon mapping of quark systems

PHYSICAL REVIEW C VOLUME 50, NUMBER 1 JULY 1994 Consistent baryon mapping of quark systems S. Pittel Bartol Research Institute, University of Delaware, Newark, Delaware 19716 J.M.

### (Dated: Accepted for publication in Reviews of Modern Physics

B. Symmetry groups and dynamical groups A symmetry group of a system is, by deﬁnition, agroup of transformations of the system that leave its Hamilto-nian invariant. For example, a symmetry group for a system with a Hamiltonian that is rotationally invariant is the rotation group SO(3) (or SU(2) if particles with in-trinsic spin are involved).

### sdg Interacting boson model: hexadecupole degree of freedom

A = 20- 80 nuclei); (vi) spdf (or sdf) boson model to describe octupole collective states; (vii) extension to odd-mass nuclei via interacting boson fermion model (IBFM) where the single particle (fermion) degree of freedom is coupled to the collective

### Spin Chains with Dynamical Lattice Supersymmetry

fermion models will serve as a great source of inspiration. The prime example for a con-nection between the two worlds is the spin-1/2 XXZ chain with anisotropy =−1/2 whose continuum limit corresponds to a superconformal ﬁeld theory with central charge c =1 (a free boson, compactiﬁed at a special radius). Using a mapping to the M 1 model,

### Ferromagnetism in the two-dimensional periodic Anderson model

a much smaller doping range than suggested by recent slave boson and dynamical mean-ﬁeld theory calcula-tions, but they were consistent with that obtained by density-matrix renormalization group calculations of the one-dimensional periodic Anderson model. DOI: 10.1103/PhysRevB.63.184428 PACS number~s!: 75.10.Jm, 71.28.1d I. INTRODUCTION

### List of publications

Boson mappings of the fermion dynamical symmetry model. Phys. Rev. C 50 (1994) 784-794. 46. P. Navrátil, H.B. Geyer, J. Dobeš, J. Dobaczewski: SDG fermion-pair algebraic SO(12) and Sp(10) models and their boson realizations. Ann. of Phys. (N.Y.) 243 (1995) 218-246. 47. J. Dobeš: F-spin mixing and M1 properties of the low-lying states in the

### Kondo physics and dissipation: A numerical renormalization

treatment of the spin-boson model via a pure-bosonic NRG.44,45 The latter has provided a good account of the criti-cal properties of the SBM for both Ohmic and sub-Ohmic bath spectra. This paper reports a direct study of the Bose-Fermi Kondo model using an NRG method extended to handle si-multaneously both fermionic and bosonic degrees of free-dom.

### Lie Groups - CoAS Drexel University

6.1 Boson Operator Algebras 98 6.2 Fermion Operator Algebras 99 14.6 Dynamical Symmetry SO(4) 261 14.9.2 Dynamical Mappings 271