Energy methods for Dirac-type equations in two-dimensional Minkowski space

Letters in Mathematical Physics - In this article, we develop energy methods for a large class of linear and nonlinear Dirac-type equations in two-dimensional Minkowski space. We will derive...     

Some global solutions of the Yang-Mills equations in Minkowski space

A class of global solutions of the Yang-Mills equations whose Cauchy data depend on a pair of arbitrary functions is constructed. The asymptotic propagation of the energy in space-time is studied. The same results are valid if the Yang-Mills field is coupled to a scalar field.Research supported in part by NSF Grants MCS 77-01340 and MCS 79-01965     

Meron-antimeron solution in Minkowski space

An elementary derivation, using Witten's Ansatz, is given of the elliptic meron-antimeron solution of the (Minkowski) SU(2) gauge theory in the W ₀=0 gauge.     

Quantum complex Minkowski space

The complex Minkowski phase space has the physical interpretation of the phase space of the scalar massive conformal particle. The aim of the paper is the construction and investigation of the quantum complex Minkowski space.     

Solving Bethe-Salpeter equation in Minkowski space

We develop a new method of solving the Bethe-Salpeter (BS) equation in Minkowski space. It is based on projecting the BS equation on the light-front (LF) plane and on the Nakanishi integral representation of the BS amplitude. This method is valid for any kernel given by the irreducible Feynman graphs. For massless ladder exchange, our approach reproduces analytically the Wick-Cutkosky equation. For massive ladder exchange, the numerical results coincide with the ones obtained by Wick rotation.     

Conformal gauge fixing in Minkowski space

Conformal gauge fixing on simply connected parts of world sheets in Minkowski space is examined in detail. It is proved that conformal gauge fixing can be imposed, including the usual boundary conditions.     

Compact topologies on Minkowski space

Minkowski space can be given topologies which are compact and which have, as their homeomorphism group, the inhomogeneous Lorentz group together with dilatations.     

q-deformed Lorentz-algebra in Minkowski phase space

In the present paper we show that the Lorentz algebra as defined in [5] is isomorphic to an algebra closely related to a q-deformed algebra. On this algebra we define a Hopf algebra structure and show its action on q-spinor modules. This algebra is related to the q-deformed Minkowski space algebra by a non invertible factorisation. Received: 12 June 1998 / Published online: 5 October 1998     

Asymptotic properties of the solutions of linear and nonlinear spin field equations in Minkowski space

In this paper I will first derive, based on energy estimations and geometric invariance, the asymptotic behavior of solutions of linear spin field equations in Minkowski space. It generalizes the result in [3] where it was proved for the spin-1 and spin-2 cases. The techniques are then applied to Yang-Mills equations, the result improves the previous one in [1] by allowing the initial data to have charge, dipole and quadrupole moments. The Lie derivative operator for spinors and some properties will be also discussed; they can be used to simplify some algebraic calculations of [4].This research is partially supported by a grant from NSF under DMS-8610730     

Cosmological constant and Minkowski space

Using the framework of classical gravitational field theory, it is shown that the equations of Einstein’s General Relativity with a cosmological constant, if requested to be compatible with the Minkowski space, change form and become the equations of Relativistic Theory of Gravitation. These equations, in contrast to General Relativity, lead us to fundamentally different physical conclusions about the Universe’s evolution and Collapse.     

Causal logic of Minkowski space

It is shown that double-orthogonal sets (diamonds) in Minkowski space form an orthomodular complete lattice. Connection with empirical logic of Randall and Foulis is discussed.     

On time-like Willmore surfaces in Minkowski space

We study time-like surfaces in Minkowski space, which are critical points of the Willmore energy. Transforming the fourth order Willmore equation into a quasi-linear, second order hyperbolic system, we prove existence, uniqueness and symmetry properties of such surfaces, subject to geometric initial conditions.     

Finite-temperature quantum field theory in Minkowski space

We formulate finite-temperature quantum field theories in Minkowski space (real time) using Feynman path integrals. We show that at non-zero temperature a new field arises which plays the role of a ghost field and is necessary for unambiguous Feynman rules. Consequently, the finite-temperature Lagrangian is different from the zero-temperature one and a new, discrete Z₂ symmetry arises. We discuss the functional formalism and spontaneous symmetry breakdown at finite temperature and also the possibility of spontaneous breakdown of the (thermal) Z₂ symmetry.     

From unstable Minkowski space to inflation

We present a perturbative approach to the equations describing the behavior of a quantum scalar field in a self-consistently generated Robertson-Walker universe. This approach throws new light on the significance of the Minkowskian instability and on the subtraction procedure which shows that a inflation cosmology is a possible future of the Minkowski space.     

Quantum deformation of compactified Minkowski space

The quantum GrassmanianG(2|0; ? _q ^4|0 ) of “quantum 2-planes ? _q ^2|0 in the quantum 4-plane ? _q ^4|0 ”, which provides aq-deformation of compactified complexified Minkowski space, is proposed. A quantum analogue of classical Plücker embedding of the usual GrassmanianG(2; ?²) into a non-degenerate quadric in ??⁵ is found.     

The Zeeman-order topology on Minkowski space

The order topology on Minkowski Space generated by Zeeman's causal order is an elementary example of a topology whose autohomeomorphism group is a Poincaré dilation group.     

From empty Minkowski space towards big-bang singularity

A new self-consistent cosmological history is exhibited in which the matter-gravitational field system evolves smoothly from a quantum unstable Minkowski vacuum towards a big-bang configuration.