Matter as Spectrum of Spacetime Representations

Bound and scattering state Schrödinger functions of nonrelativistic quantum mechanics as representation matrix elements of space and time are embedded into residual representations of spacetime as generalizations of Feynman propagators. The representation invariants arise as singularities of rational representation functions in the complex energy and complex momentum plane. The homogeneous space GL(²)U(2) with rank 2, the orientation manifold of the unitary hypercharge-isospin group, is taken as model of nonlinear spacetime. Its representations are characterized by two continuous invariants whose ratio will be related to gauge field coupling constants as residues of the related representation functions. Invariants of product representations define unitary Poincaré group representations with masses for free particles in tangent Minkowski spacetime.     

Spinor brane

The thick brane model supported by a nonlinear spinor field is constructed. The different cases with the various values of the cosmological constant ${\Lambda \left( {l} < \\ =\\ > \right) 0}${\Lambda \left( \begin{array}{l} < \\ =\\ > \end{array} \right) 0} are investigated. It is shown that regular analytical spinor thick brane solutions with asymptotically Minkowski (at Λ = 0) or anti-de Sitter spacetimes (at Λ <  0) do exist.     

Spinor geometry

In this paper the construction of the geometry begins with the assignment of a spinor (spinor ether) and the coordinates x are constructed as a spinor product. It is shown that the corresponding space is a Friedmann space and the coordinates x are Friedmann coordinates. The system of gravitational and field equations is closed. The theory contains eight real functions which specify both the reference system and the coordinate grid. The theory admits quantization of space-time and is free of the difficulties associated with inertia and the absolute character of flat space-time.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 7–12, February, 1977.     

Spinor Relativity

Spinor relativity is a unified field theory, which derives gravitational and electromagnetic fields as well as a spinor field from the geometry of an eight-dimensional complex and ‘chiral’ manifold. The structure of the theory is analogous to that of general relativity: it is based on a metric with invariance group GL(ℂ²), which combines the Lorentz group with electromagnetic U(1), and the dynamics is determined by an action, which is an integral of a curvature scalar and does not contain coupling constants. The theory is related to physics on spacetime by the assumption of a symmetry-breaking ground state such that a four-dimensional submanifold with classical properties arises. In the vicinity of the ground state, the scale of which is of Planck order, the equation system of spinor relativity reduces to the usual Einstein and Maxwell equations describing gravitational and electromagnetic fields coupled to a Dirac spinor field, which satisfies a non-linear equation; an additional equation relates the electromagnetic field to the polarization of the ground state condensate.     

Spinor structure of space-time

The spinor structure on space-time manifold is investigated in the frame of Crumeyrolle's approach. Some of his theorems are simplified. The equivalence of this approach to the Milnor and Lichnerowicz one is shown using topological properties of the group space of ₀. The equivalence of any two spinor structures on simply connected space-time is established.Partly supported by the Polish Government under the Research Program MR I.7.     

Spinor Factorizations for Relativity

Factorization of 2-component spinors in the mathematical language of General Relativity is often the starting point of classifications of them. Particular factorizations for the Ricci and Weyl spinors are well known. The determination of factorizations of (p, q) spinors is equivalent to the determination of double or bipartite partitions. Firstly a technique for enumeration of such partitions is given, with explicit calculations up to (4, 4). Secondly a method is devised to actually obtain the factorizations, display them for the Ricci, Weyl and Lanczos-Zund spinors, and then reference the full tabulation up to (4, 4) spinors—the most useful for Relativity.     

Spinor Field Nonlinearity and Space-Time Geometry

Within the scope of Bianchi type VI,VI0,V, III, I, LRSBI and FRW cosmological models we have studied the role of nonlinear spinor field on the evolution of the Universe and the spinor field itself. It was found that due to the presence of non-trivial non-diagonal components of the energy-momentum tensor of the spinor field in the anisotropic space-time, there occur some severe restrictions both on the metric functions and on the components of the spinor field. In this report we have considered a polynomial nonlinearity which is a function of invariants constructed from the bilinear spinor forms. It is found that in case of a Bianchi type-VI space-time, depending of the sign of self-coupling constants, the model allows either late time acceleration or oscillatory mode of evolution. In case of a Bianchi VI₀ type space-time due to the specific behavior of the spinor field we have two different scenarios. In one case the invariants constructed from bilinear spinor forms become trivial, thus giving rise to a massless and linear spinor field Lagrangian. This case is equivalent to the vacuum solution of the Bianchi VI₀ type space-time. The second case allows non-vanishing massive and nonlinear terms and depending on the sign of coupling constants gives rise to accelerating mode of expansion or the one that after obtaining some maximum value contracts and ends in big crunch, consequently generating space-time singularity. In case of a Bianchi type-V model there occur two possibilities. In one case we found that the metric functions are similar to each other. In this case the Universe expands with acceleration if the self-coupling constant is taken to be a positive one, whereas a negative coupling constant gives rise to a cyclic or periodic solution. In the second case the spinor mass and the spinor field nonlinearity vanish and the Universe expands linearly in time. In case of a Bianchi type-III model the space-time remains locally rotationally symmetric all the time, though the isotropy of space-time can be attained for a large proportionality constant. As far as evolution is concerned, depending on the sign of coupling constant the model allows both accelerated and oscillatory mode of expansion. A negative coupling constant leads to an oscillatory mode of expansion, whereas a positive coupling constant generates expanding Universe with late time acceleration. Both deceleration parameter and EoS parameter in this case vary with time and are in agreement with modern concept of space-time evolution. In case of a Bianchi type-I space-time the non-diagonal components lead to three different possibilities. In case of a full BI space-time we find that the spinor field nonlinearity and the massive term vanish, hence the spinor field Lagrangian becomes massless and linear. In two other cases the space-time evolves into either LRSBI or FRW Universe. If we consider a locally rotationally symmetric BI(LRSBI) model, neither the mass term nor the spinor field nonlinearity vanishes. In this case depending on the sign of coupling constant we have either late time accelerated mode of expansion or oscillatory mode of evolution. In this case for an expanding Universe we have asymptotical isotropization. Finally, in case of a FRW model neither the mass term nor the spinor field nonlinearity vanishes. Like in LRSBI case we have either late time acceleration or cyclic mode of evolution. These findings allow us to conclude that the spinor field is very sensitive to the gravitational one.     

Gravitational Interactions in the Dirac Spinor Fields and Possible Structure of Local Space-Time of Fermions

Russian Physics Journal - Within the framework of general relativity, possible effects of the gravitational interactions in the Dirac spinor field are considered. It is shown that these...     

Spinor field and nonmetricity of space-time

A study is made of the dynamics of a self-gravitating spinor field in a space with curvature and nonmetricity. It is shown that the nonmetricity of the space-time may induce a vector nonlinearity of cubic type in the equation of the spinor field. Also possible is the opposite effect in which such a nonlinearity of the spinor equation is compensated by the influence of the nonmetricity of space-time.Translated from Izvestiya Vysshikh Uchebnykh. Zavedenii, Fizika, No. 6, pp. 52–55, June, 1980.     

Spinor fields and symmetries of the spacetime

We show that in the background of a stationary and axisymmetric black hole, there is a particular spinor field whose “conserved current” interpolates between the null Killing vector on the horizon and the time Killing vector at the spatial infinity. The spinor field only needs to satisfy a very general and simple constraint.     

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     

A Spinor from Semiderivatives

Fractional derivatives have been known since the time of Leibniz and have been used in various branches of physics. The present paper shows how they can be used to generate a spinor field, much as the gradient operator generates a vector field. These spinor fields are zero kinetic energy solutions to the Dirac equation.     

Structure of Nuclear Matter at Short Distances

Physics of Atomic Nuclei - In the past decades, considerable advances have been made both in experimentally studying and in theoretically describing properties of cold nuclear matter at short...     

Spinor Decomposition of SU（2） Gauge Potential and Spinor Structures of Chern-Simons and Chern Density

In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinor is studied. Using this decomposition, the spinor structures of Chern Simons form and the Chern density are obtained. Furthermore, the knot quantum number of non-Abelian gauge theory can be expressed by the Chern-Simons spinor structure, and the second Chern number is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.     

Spinor Decomposition of SU(2) Gauge Potential and Spinor Structures of Chern-Simons and Chern Density

In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinor is studied. Using thisdecomposition, the spinor structures of Chern-Simons form and the Chern density are obtained. Furthermore, the knotquantum number of non-Abelian gauge theory can be expressed by the Chern-Simons spinor structure, and the secondChern number is characterized by the Hopf indices and the Brouwer degrees of φ-mapping.