Soliton Dynamics in a 4D Nonlinear Spinor Field Model under White Noise

Physics of Particles and Nuclei Letters - In this paper, we investigate the soliton solutions of a 4D nonlinear pure spinor fermionic model with forcing and damping under white noise to understand...     

Quantization of superparametrized monopoles

Classical finite-energy solutions of the SU(2) Yang-Mills-Higgs system in four-dimensional space-time are embedded in the supersymmetric extension of the theory. Finite supertranslations are constructed and are used to obtain a family of solutions to the supersymmetric field equations, parametrized by fermionic Majorana spinor parameters. The quantum theory around arbitrary classical solutions, parametrized by arbitrary bosonic (global and local) as well as fermionic (global) parameters, is constructed and discussed.     

Fermions without spinors

The classical Kähler equation for an inhomogeneous differential form is analysed in some detail with respect to the physical properties of its Minkowski space solutions. Although the components of the field contain only integer representations of the Lorentz group for a physical interpretation of the quantum theory, we impose fermionic commutators. The electromagnetic interactions are identical to those of a Dirac spinor field with an extra fourfold degeneracy. Possibilities for the interpretation of the extra degrees of freedom are discussed.     

Compactification and signature transition in Kaluza-Klein spinor cosmology

We study the classical and quantum cosmology of a 4 + 1-dimensional space-time with a non-zero cosmological constant coupled to a self-interacting massive spinor field. We consider a spatially flat Robertson-Walker universe with the usual scale factor R (t) and an internal scale factor a (t) associated with the extra dimension. For a free spinor field the resulting equations admit exact solutions, whereas for a self-interacting spinor field one should resort to a numerical method for exhibiting their behavior. These solutions give rise to a degenerate metric and exhibit signature transition from a Euclidean to a Lorentzian domain. Such transitions suggest a compactification mechanism for the internal and external scale factors such that a ∼ R⁻¹ in the Lorentzian region. The corresponding quantum cosmology and the ensuing Wheeler-DeWitt equation have exact solutions in the mini-superspace when the spinor field is free, leading to wavepackets undergoing signature change. The question of stabilization of the extra dimension is also discussed.     

Quantum cosmology with fermionic matter

The quantum evolution of homogeneous isotropic cosmological models with ferm ionic matter described by spinor fields is investigated within the framework of the formalism of superspace quantization. The fact that quadratic combinations of fermionic operators (current density, spin density, Lagrangian, etc.) are bosonic operators and admit an explicit Schrödinger representation is used in an essential way. It is shown that the DeWitt equation for the cosmological models with fermionic matter under consideration has the form of the Schrödinger equation, so that a correct definition is possible for the probability density of the existence of the models under consideration, in which the singularity is removed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 15–19, March, 1990.     

Spinors, Inflation, and Non-Singular Cyclic Cosmologies

We consider toy cosmological models in which a classical, homogeneous, spinor field provides a dominant or sub-dominant contribution to the energy-momentum tensor of a flat Friedmann-Robertson-Walker universe. We find that, if such a field were to exist, appropriate choices of the spinor self-interaction would generate a rich variety of behaviors, quite different from their widely studied scalar field counterparts. We first discuss solutions that incorporate a stage of cosmic inflation and estimate the primordial spectrum of density perturbations seeded during such a stage. Inflation driven by a spinor field turns out to be unappealing as it leads to a blue spectrum of perturbations and requires considerable fine-tuning of parameters. We next find that, for simple, quartic spinor self-interactions, non-singular cyclic cosmologies exist with reasonable parameter choices. These solutions might eventually be incorporated into a successful past- and future-eternal cosmological model free of singularities. In an Appendix, we discuss the classical treatment of spinors and argue that certain quantum systems might be approximated in terms of such fields.     

Quantum spinors and the singularity theorems of general relativity

I suggest that space-time singularities may be removed through the quantum effects of fermionic spinor matter. I support this viewpoint on the basis of an effective negative contribution, coming from spinor fields with anticommutative (“quantum”) nature, to the energy condition of the singularity theorems of general relativity.     

Three-dimensional fermionic determinants,Chern-Simons and nonlinear field redefinitions

The three-dimensional abelian fermionic determinant of a two component massive spinor in flat euclidean space-time is reset to a pure Chern-Simons action through a nonlinear redefinition of the gauge field.     

Unitarity and modular invariance as constraints on four-dimensional superstrings

It is shown that the requirements of space-time factorization for vertices and one-loop modular invariance guarantee higher-loop modular invariance (as it is presently understood) in the context of string models built out of free fermion fields, either twisted or untwisted. The general solution satisfying these requirements is derived and their relation to the conservation of quantum numbers at general fermionic vertices is discussed. A number of models are discussed using a diagrammatic notation. The natural occurrence in such models of spinor representations which have features in common with the observed quark-lepton multiplets is noted.     

Chiral invariant Gross-Neveu model: Classical versus quantum

We present a unification of different and independently investigated aspects of the chiral invariant Gross-Neveu model. Special emphasis is placed on the relevance of classical (c-number, non Grassmann) spinor solutions of the G-N field equations for the construction, and thus understanding of the respective quantized Fermi model. To get an insight into the “quantum meaning of classical field theory” if specialized to the G-N case, we perform the path integral quantization procedure which first leads to the Fermi oscillator problem, and then, after appropriate generalizations, to the quantum Fermi G-N model. Path integrals are carried out with respect to c-number spinor paths only, and in fact no reference is necessary to the Grassmann algebra methods, which are conventionally used to integrate out fermions.     

Spinor Representations of and Quantum Boson-Fermion Correspondence

This is an extension of quantum spinor construction in [DF2]. We define quantum affine Clifford algebras based on the tensor product of a finite dimensional representation and an infinite highest weight representation of and the solutions of q-KZ equations, construct quantum spinor representations of and explain classical and quantum boson-fermion correspondence. Received: 22 November 1995 / Accepted: 21 July 1998     

Time reparameterization in Bianchi type I spinor cosmology

The problem of time reparameterization is addressed at both the classical and quantum levels in a Bianchi-I universe in which the matter source is a massive Dirac spinor field. We take the scale factors of the metric as the intrinsic time and their conjugate momenta as the extrinsic time. A scalar character of the spinor field is identified as a representation of the extrinsic time. The construction of the field equations and quantization of the model is achieved by solving the Hamiltonian constraint after time identification has been dealt with. This procedure leads to a true Hamiltonian whose exact solutions for the above choices of time are presented.     

Geometry and symmetries in lattice spinor gravity

Lattice spinor gravity is a proposal for regularized quantum gravity based on fermionic degrees of freedom. In our lattice model the local Lorentz symmetry is generalized to complex transformation parameters. The difference between space and time is not put in a priori, and the euclidean and the Minkowski quantum field theory are unified in one functional integral. The metric and its signature arise as a result of the dynamics, corresponding to a given ground state or cosmological solution. Geometrical objects as the vierbein, spin connection or the metric are expectation values of collective fields built from an even number of fermions. The quantum effective action for the metric is invariant under general coordinate transformations in the continuum limit. The action of our model is found to be also invariant under gauge transformations. We observe a “geometrical entanglement” of gauge- and Lorentz-transformations due to geometrical objects transforming non-trivially under both types of symmetry transformations.     

Bosonization of supersymmetric KdV equation

Bosonization approach to the classical supersymmetric systems is presented. By introducing the multi-fermionic parameters in the expansions of the superfields, the N=1 supersymmetric KdV (sKdV) system is transformed to a system of coupled bosonic equations. The method can be applied to any fermionic systems. By solving the coupled bosonic equations, some novel types of exact solutions can be explicitly obtained. Especially, the richness of the localized excitations of the supersymmetric integrable system is discovered. The rich multi-soliton solutions obtained here have not yet been obtained by using other methods. However, the traditional known multi-soliton solutions can also not be obtained by the bosonization approach of this Letter. Some open problems on the bosonization of the supersymmetric integrable models are proposed in the both classical and quantum levels.     

Composite massless vector field obtained from fundamental fermions

From a purely fermionic dynamics an effective theory of composite bosonic fields may be derived. We concentrate on the point-splitting construction of aU(1)-gauge boson as a spinor bilinear; this proposal has been thoroughly examined before within a noncanonicalU(1)-invariant Lagrangian spinor model. We point out that the induced effective gauge coupling depends on additional regulator masses and verify that the point-splitting regularization will spoil the gauge invariance of one-loop quantum corrections containing background spinor fields. These results contradict previous work on this subject.     

On the integrability of classical spinor models in two-dimensional space-time

Well known classical spinor relativistic-invariant two-dimensional field theory models, including the Gross-Neveu, Vaks-Larkin-Nambu-Jona-Lasinio and some other models, are shown to be integrable by means of the inverse scattering problem method. These models are shown to be naturally connected with the principal chiral fields on the symplectic, unitary and orthogonal Lie groups. The respective technique for construction of the soliton-like solutions is developed.     

Classical theory of the octonian field

We develop a nonassociative classical theory of the octonion spinor field. We construct the Lagrange function, the field equations, the solutions, the energymomentum tensor, the spin, and the associator, which is a new quantum characteristic. We consider the interaction of the octonion spinor field with the electromagnetic field. We show that, in the case of a massless field, the energy, the spin, and the associator can be measured simultaneously, while in the case of a field with rest mass, only either spin and energy or spin and associator can be measured simultaneously.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 58–62, December, 1986.     

Field theory of the interacting string: The closed string

We recast dual models in the language of a quantum field theory of functional fields, restricting ourselves for simplicity to the closed string model. We derive the dynamics for both scalar and spinor functional fields from a unique parametrization invariant action. Passages to the Hamiltonian formalism and second quantization are explicitly worked out for the closed mesonic string in the front form. The results are equivalent to those obtained earlier by GGRT, i.e. no ghost fields at the price of an anomalous number of space-time dimensions and a tachyon. Finally, we use the parametrization invariance requirement on the action to derive couplings of closed strings to local fields by extending a global U(1) invariance built in the free action into a local one in the functional sense. We construct the self-couplings of closed string fields by requiring these to be consistent with the gauge invariance of the external fields. This procedure uniquely leads (for the open string) to the string splitting picture of Nambu and Mandelstam. The closed string is found to cross itself and then split up into two others. Both open and closed strings have quartic interactions corresponding to strand (for the open string) and lobe (for the closed string) exchanges. The case of the interacting fermionic model is not treated here.