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.     

Discrete dynamical equations in Minkowski space

Discrete difference equations in Minkowski space are obtained and the discrete Minkowski force is shown to be a four-vector. A transformation from a discrete dynamical equation in Minkowski space to a Lorentz-invariant difference equation in one-dimensional space is given.     

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     

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.     

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.     

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.     

The cohomology of nets over Minkowski space

We investigate the cohomology of nets over Minkowski space and develop exact sequence techniques enabling us to compute many low-dimensional cohomologies. We examine in particular nets derived from smooth solutions of invariant partial differential equations using causal support conditions. Thus the wave equation gives a trivial second cohomology whereas the vector wave equation with Lorentz condition and Maxwell's equations give a second cohomology and × corresponding, respectively, to an electric and an electric and magnetic charge.     

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.     

Symmetric and traceless tensors on Minkowski space

The symmetric traceless projection of a tensor of rank 2l on Minkowski space is determined. These tensors form an invariant subspace under transformations by the 2l-fold product of an element of the Lorentz group SO₀(1, 3). As is well known, this representation is irreducible and equivalent to the representation (l₁,l₂) of the group $\text{SL(}\text{2,C}\text{)}$ for l₁ = l₂ = l. We derive the explicit form of the equivalence operator and its main properties. With these investigations we extend results obtained by S. Weinberg.     

Spinor analysis of Yang-Mills theory in the Minkowski space

Self-duality equations for Yang-Mills fields and the Dirac equation with an external (anti-) selfdual gauge field are studied in the Minkowski space by spinorial methods. For the Dirac equations, all (four) possible combinations of the fermion chirality and duality of the external fields are considered.     

An algebraic characterization of vacuum states in Minkowski space

An algebraic characterization of vacuum states on nets ofC ^*-algebras over Minkowski space is given and space-time translations are reconstructed with the help of the modular structures associated with such states. The result suggests that a condition of geometrical modular action might hold in quantum field theories on a wider class of spacetime manifolds.