Boson-fermion Coupling Research Articles

On hidden broken nonlinear superconformal symmetry of conformal mechanics and nature of double nonlinear superconformal symmetry

We show that for positive integer values l of the parameter in the conformal mechanics model the system possesses a hidden nonlinear superconformal symmetry, in which reflection plays a role of the grading operator. In addition to the even so(1,2)⊕u(1)-generators, the superalgebra includes 2l+1 odd integrals, which form the pair of spin-(l+12) representations of the bosonic subalgebra and anticommute for order 2l+1 polynomials of the even generators. This hidden symmetry, however, is broken at the level of the states in such a way that the action of the odd generators violates the boundary condition at the origin. In the earlier observed double nonlinear superconformal symmetry, arising in the superconformal mechanics for certain values of the boson–fermion coupling constant, the higher order symmetry is of the same, broken nature.

Superconformal mechanics and nonlinear supersymmetry

We show that a simple change of the classical boson-fermion coupling constant, $2\alpha \to 2\alpha n $, $n\in \N$, in the superconformal mechanics model gives rise to a radical change of a symmetry: the modified classical and quantum systems are characterized by the nonlinear superconformal symmetry. It is generated by the four bosonic integrals which form the so(1,2) x u(1) subalgebra, and by the 2(n+1) fermionic integrals constituting the two spin-n/2 so(1,2)-representations and anticommuting for the order n polynomials of the even generators. We find that the modified quantum system with an integer value of the parameter $\alpha$ is described simultaneously by the two nonlinear superconformal symmetries of the orders relatively shifted in odd number. For the original quantum model with $|\alpha|=p$, $p\in \N$, this means the presence of the order 2p nonlinear superconformal symmetry in addition to the osp(2|2) supersymmetry.

Collective excitations in trapped boson-fermion mixtures: From demixing to collapse

We calculate the spectrum of low-lying collective excitations in a gaseous cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas over a range of the boson-fermion coupling strength extending from strongly repulsive to strongly attractive. Increasing boson-fermion repulsions drives the system towards spatial separation of its components (``demixing''), whereas boson-fermion attractions drives it towards implosion (``collapse''). The dynamics of the system is treated in the experimentally relevant collisionless regime by means of a random-phase approximation, and the behavior of a mesoscopic cloud under isotropic harmonic confinement is contrasted with that of a macroscopic mixture at given average particle densities. In the latter case the locations of both the demixing and the collapse phase transitions are sharply defined by the same stability condition, which is determined by the softening of an eigenmode of either fermionic or bosonic origin. In contrast, the transitions to either demixing or collapse in a mesoscopic cloud at fixed confinement and particle numbers are spread out over a range of boson-fermion coupling strength, and some initial decrease of the frequencies of a set of collective modes is followed by hardening, as evidenced by blue shifts of most eigenmodes. The spectral hardening can serve as a signal of the impending transition and is most evident when the number of bosons in the cloud is relatively large. We propose physical interpretations for these dynamical behaviors with the help of suitably defined partial compressibilities for the gaseous cloud under confinement.

Feshbach resonance described by boson-fermion coupling

We consider a possibility to describe the Feshbach resonance in terms of the Boson Fermion (BF) model. Using such model we show that after a gradual disentangling of the boson from fermion subsystem the resonant type scattering between fermions is indeed generated. We decouple the subsystems via: (a) the single step, and (b) the continuous canonical transformation. With the second one we investigate the feedback effects effectively leading to the finite amplitude of the scattering strength. We study them in detail in: the normal $T>T_{c}$ and superconducting $T \leq T_{c}$ states.

Collective excitations of a trapped boson-fermion mixture across demixing

We calculate the spectrum of low-lying collective excitations in a mesoscopic cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas as a function of the boson-fermion repulsions. The cloud is under isotropic harmonic confinement and its dynamics is treated in the collisional regime by using the equations of generalized hydrodynamics with inclusion of surface effects. For large numbers of bosons we find that, as the cloud moves towards spatial separation (demixing) with increasing boson-fermion coupling, the frequencies of a set of collective modes show a softening followed by a sharp upturn. This behavior permits a clear identification of the quantum phase transition. We propose a physical interpretation for the dynamical transition point in a confined mixture, leading to a simple analytical expression for its location.

Collisionless and hydrodynamic excitations of trapped boson-fermion mixtures

Within a scaling ansatz formalism plus Thomas-Fermi approximation, we investigate the collective excitations of a harmonically trapped boson-fermion mixture in the collisionless and hydrodynamic limit at low temperature. Both the monopole and quadrupole modes are considered in the presence of spherical as well as cylindrically symmetric traps. In the spherical traps, the frequency of monopole mode coincides in the collisionless and hydrodynamic regime, suggesting that it might be undamped in all collisional regimes. In contrast, for the quadrupole mode, the frequency differs largely in these two limits. In particular, we find that in the hydrodynamic regime the quadrupole oscillations with equal bosonic and fermionic amplitudes generate an exact eigenstate of the system, regardless of the boson-fermion interaction. This resembles the Kohn mode for the dipole excitation. We discuss in some detail the behavior of monopole and quadrupole modes as a function of boson-fermion coupling at different boson-boson interaction strength. Analytic solutions valid at weak and medium fermion-boson coupling are also derived and discussed.

Effective Gauge Theories with Symmetry Breaking

Abstract In a previous paper a general group theoretical discussion of effective boson-fermion coupling theories (with com posite two-fermion bosons) resulting by weak mapping of nonlinear spinor-isospinor field models was given. In the present work these considerations are extended to the case of broken isospin symmetry and applied to a microscopic subfermion-description of phenomenolog­ical gauge theories with Higgs symmetry breaking.

Effective Boson-Fermion Dynamics for Subfermion Models

Abstract Effective composite particle dynamics can be derived by weak mapping of quantum fields. This method was already applied to derive effective boson or boson-fermion coupling theories from a nonlinear subfermion field. In this paper we present an extension of those calculations to the general group theoretical treatm ent of two-fermion bound states and their coupling to (elementary) fermions within an arbitrary nonlinear spinor-isospinor field model. The resulting effective field equations are com pared with the corresponding phenomenological expressions which for example underly the standard electroweak theory. PACS 11 .10 - Field theory. PACS 12.10 - Unified field theories and models. PACS 12.35 - Composite models of particles.

The vacuum structure in scalar bidimensional models with ø4 and ø6 self-interactions. A lattice study

The vacuum structure of a bidimensional model including a real scalar field with quartic and sextic self-interacting terms is analyzed on a lattice. Starting from a classical potential with three equivalent minima the quantum corrections modify the tree-level picture so that as a last resort the vacuum is unique. Eventually we briefly discuss the effect of introducing a Yukawa boson-fermion coupling.

On the theory of composite gauge bosons: Calculation of coupling constants and covariant derivatives

In preceding papersSU(2) gauge bosons were derived as two-fermion composites from a regularized non-linear spinor-isospinor field model and it was demonstrated that in the low-energy limit the corresponding Yang-Mills dynamics in temporal gauge is reproduced as an effective theory. In this paper we calculate the effective interactions of these compositeSU(2) gauge bosons with the elementary fermions of the model, which lead to minimal gauge covariant coupling. The consideration of a combined boson-fermion system instead of a pure boson system allows the determination of the correspondingSU(2) boson-boson coupling constant as well as the boson-fermion coupling constant.

ON THE VACUUM STABILITY IN THE SUPERRENORMALIZED YUKAWA-TYPE THEORY

The stability of the ground state and the possibility of the appearance of a phase transition in the superrenormalizable nonlocal Yukawa-type field theory are investigated. A variational estimation of the upper bound for the effective potential is obtained. It is shown that there exists a finite critical value for the boson-fermion coupling constant. The initial vacuum becomes unstable when this coupling constant exceeds the critical value. As a result, the system under consideration goes into the phase with nonvanishing expectation value of the field.

Formfactors of Relativistic Composite Particle Interactions in Unified Nonlinear Spinorfield Models

Unified nonlinear spinorfield models are self-regularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined and below the threshold of preon production the effective dynamics of the model is only concerned with bound state reactions. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived and the effective dynamics for preon-antipreon boson states and three preon-fermion states (with corresponding anti-fermions) was studied in the low energy limit. The transformation of the functional energy representation of the spinorfield into composite particle functional operators produced a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. In this paper these calculations are extended into the high energy range. This leads to formfactors for the composite particle interaction terms which are calculated in a rough approximation and which in principle are observable. In addition, the mathematical and physical interpretation of nonlocal quantum field theories and the meaning of the mapping procedure, its relativistic invariance etc. are discussed.

Effective Interactions of Relativistic Composite Particles in Unified Nonlinear Spinor-Field Models. III

Unified nonlinear spinor field models are selfregularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined. In preceding papers a functional energy representation, the statistical interpretation and the dynamic equations were derived. In this paper the dynamics of composite particles is discussed. The composite particles are defined to be eigensolutions of the diagonal part of the energy representation. Corresponding calculations are in preparation, but in the present paper a suitable composite particle spectrum is assumed. It consists of preon-antipreon boson states and threepreon- fermion states with corresponding antifermions and contains bound states as well as preon scattering states. The state functional is expanded in terms of these composite particle states with inclusion of preon scattering states. The transformation of the functional energy representation of the spinor field into composite particle functional operators produces a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. This representation is valid as long as the processes are assumed to be below the energetic threshold for preon production or preon break-up reactions, respectively. From this it can be concluded that below the threshold the effective interactions of composite particles in a unified spinor field model lead to phenomenological coupling theories which depend in their properties on the bound state spectrum of the self-regularizing spinor theory.

Effective Interactions of Relativisic Composite Particles in Unified Nonlinear Spinor-Field Models. II

Unified nonlinear spinor field models are selfregularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived. In this paper the dynamics of composite particles is discussed. The composite particles are defined to be eigensolutions of the diagonal part of the energy representation. Corresponding calculations are in preparation, but in the present paper a suitable composite particle spectrum is assumed. It consists of preon-antipreon boson states and threepreon- fermion states with corresponding antifermions and contains bound states as well as preon scattering states. The state functional is expanded in terms of these composite particle states with inclusion of preon scattering states. The transformation of the functional energy representation of the spinor field into composite particle functional operators produces a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. This representation is valid as long as the processes are assumed to be below the energetic threshold for preon production or preon break-up reactions, respectively. From this it can be concluded that below the threshold the effective interactions of composite particles in a unified spinor field model lead to phenomenological coupling theories which depend in their properties on the bound state spectrum of the self-regularizing spinor theory.

Effective Interactions of Relativistic Composite Particles in Unified Nonlinear Spinor-Field Models. I

Unified nonlinear spinor field models are selfregularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived. In this paper the dynamics of composite particles is discussed. The composite particles are defined to be eigensolutions of the diagonal part of the energy representation. Corresponding calculations are in preparation, but in the present paper a suitable composite particle spectrum is assumed. It consists of preon-antipreon boson states and threepreon- fermion states with corresponding antifermions and contains bound states as well as preon scattering states. The state functional is expanded in terms of these composite particle states with inclusion of preon scattering states. The transformation of the functional energy representation of the spinor field into composite particle functional operators produces a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. This representation is valid as long as the processes are assumed to be below the energetic threshold for preon production or preon break-up reactions, respectively. From this it can be concluded that below the threshold the effective interactions of composite particles in a unified spinor field model lead to phenomenological coupling theories which depend in their properties on the bound state spectrum of the self-regularizing spinor theory.