Space-time geometry and symmetry breaking

We look for solutions of the Einstein-Yang-Mills equations in a 4 + D dimensional space-time. We find solutions where the first 4 dimensions are a flat Minkowskian space-time, while the D others are a compact, space-like manifold of small size. Such solutions can be obtained for an arbitrary compact gauge group K and are invariant under a sub-group G of K related to the space-time geometry. This shows that 4 + D dimensional gravity can give a mechanism for the super-strong symmetry breaking needed in grand unified field theories without introducing Higgs scalars.     

Space-time and holonomy groups

The possibilities for the (full) holonomy group of a (simply connected) vacuum space-time are calculated. The non-simply connected case is also discussed.     

Space-time symmetries in gauge theories

A general definition of symmetries of gauge fields is proposed and a method developed for constructing symmetric fields for an arbitrary gauge group. Scalar fields occur naturally in the formalism and the pure gauge theory reduces to a Higgs model in lower dimensions.Laboratoire propre du C.N.R.S. associé à l'Ecole Normale Supérieure et à l'Université de Paris Sud     

Lattice gauge-higgs theories with local x global symmetry groups including exact solutions

We discuss a class of lattice gauge-Higgs models with local x global symmetry groups. These may also be viewed as a new class of disordered spin models. We give general properties of these theories and present exact solutions for certain (infinite) classes of discrete 2D models. Given the strong gauge coupling limit involved, the latter constitute the first nontrivial exactly solved gauge-Higgs theories. Our results provide the first existence proof of theories which satisfy a necessary condition of realistic gauge-Higgs models, namely that the mass gaps for the Higgs and gauge sectors must both vanish and their ratio must approach a finite constant, in the continuum limit.     

Broken symmetry of lie groups of transformation generating general relativistic theories of gravitation

Intransitive Lie groups of transformations have invariant varieties which in suitable cases can be considered as space-times of a universe. The physical laws in the latter are expressed in terms of group theoretical notions. Theorems on the coincidences of group trajectories and geodesics are derived. The groups of linear transformations of the space of basis vectors are used as gauge groups to break the symmetry of the group of transformations and of their natural metric. It is shown that in case of the de Sitter group and its adjoint group as gauge group, one obtains in this way general relativistic theories of gravitation, especially Einstein's theory. More general aspects of the formalism are discussed.Article written in memoriam of B. Jouvet of the Collège de France     

Space-time groups for the lattice

In the assumption of a lattice theory in which the continuous limit is not taken, the metric of the discrete space-time should be invariant under integral transformations. Based on local isomorphisms between real forms, a method is proposed in order to find the rational and integral elements of the pseudoorthogonal groups. Besides, the rational and integral trigonometric and hyperbolic functions are constructed on the lattice.The ideas in this paper were presented in the VI Seminar on Quantum Theory and the Structure of Space and Time, Tutzing, July 1984.     

Space-time resolved approach for interacting quantum field theories

An alternative approach to the usual perturbative S-matrix evaluation of quantum field theories is presented which is nonperturbative and provides full space-time resolution. We study the dynamical development of the force between two fermion wave packets for the Yukawa system. The spatial distribution of the virtual bosons that act as mediators of the force can be analyzed along with the fermionic densities. Using a potential function for the fermion-fermion interaction is a good approximation to the field theoretical calculations when the Fock space is restricted to only one boson, but in the full quantum field theory the fermion-fermion force is enhanced by higher-order multiboson processes. Furthermore, the normally attractive fermion-fermion Yukawa force can, in principle, be manipulated to even be repulsive if the momentum modes available to the virtual bosons are restricted.     

Accidental degeneracies and symmetry groups

It is usually assumed that the appearance of accidental degeneracy in the energy levels of a given Hamiltonian is due to a symmetry group. By considering the elementary problem of a rotator with spin-orbit coupling, when the strength of the latter is equal to the inverse of the moment of inertia, we find that this assumption does not explain the degeneracy of all the levels of the Hamiltonian. Thus the relation between accidental degeneracies and symmetry group merits further probing.     

Lie groups and gravity theories

Generalized theories of gravitation using the group manifold approach are outlined. It is suggested that free differential algebras should take the place of Lie algebras in current physical theory.     

Objective local theories and the symmetry between analyzers

It is shown that a necessary condition for objective local theories to be equivalent to quantum mechanics in correlation experiments in the existence of a dissymmetry between analyzers or, alternately, a space anisotropy. No supplementary assumption is made about detection probabilities when the variables of the local theory all lie in the plane of the analyzers. The proof extends to three-dimensional variables if one supposes the detection process to be free of instabilities.     

Degrees of symmetry in quantum field theories

A hierarchy of possible symmetries in quantum field theory is defined, which reaches from a purely mathematical invariance to the conventional physical invariance, including the commonly discussed type of spontaneously broken symmetry (SBS). It is shown that one type of SBS, which is usually not considered, naturally leads to theories with an algebra of non-conserved currents and a non-linearly transforming phenomenological Lagrangian. An exactly solvable model is given and some general remarks are made.     

Field dependent nilpotent symmetry for gauge theories

We present predictions for the inclusive production of D mesons at the CERN LHC in the general-mass variable-flavor-number scheme at next-to-leading order. Detailed numerical results are compared to data where available, or presented in a way to ease future comparisons with experimental results. We also point out that measurements at large rapidity have the potential to pin down models of intrinsic charm.     

Infinite symmetry algebras of extended supergravity theories

When extended supergravity theories with noncompact symmetry groups are written in a physical gauge, the noncompact symmetries join with the supersymmetries to generate an infinite-dimensional algebra. The details are worked out explicitly for a two-dimensional theory with an SU(1, 1) internal symmetry. Our analysis confirms the observation of Ellis et al. that the infinite rigid superalgebra should be obtained from the finite-dimensional local superalgebra by replacing scalar fields with their asymptotic values at infinity. The infinite algebra is described by extending the super-Poincaré generators to functions on the coset space defined by the scalar fields at infinity. While mathematically nontrivial, this result is, in a certain sense, trivial from a physical point of view.     

Left-right symmetry breaking scale and supersymmetry in unified theories

We propose a class of supersymmetric grand unified models where parity and SU(2)_R breaking scales are widely separated and compatible with a low-lying mass for the right-handed gauge boson W_R. The intermediate symmetry SU(4)_c×SU(2)_L×SU(2)_R and Higgs content are uniquely fixed if m_WR < 10⁹ GeV. The unification scale lies within an order of magnitude below the Planck mass.     

Colour symmetry double point groups

Thirty four distinct composition series arising out of the 32 crystallographic double point groups are employed to re-derive in a simple and elegant fashion all the 169 distinct colour symmetry groups generated by the 32 double point groups, exploiting the idea of colour generators. The advantage of the method employed and some possible applications of these colour groups are discussed. The resulting colour groups are tabulated.     

Non-compact intrinsic symmetry groups and many-particle states

It is argued that a non-compact group describing an intrinsic symmetry of elementary particles should posses the following property: There exists a subsetΦ of all the unitary irreducible representations such that for any two representations ofΦ the Kronecker product decomposes into a directsum of representations ofΦ only. By this criterium the groups SL(n, C) are excluded. The coupling of unitary irreducible representations of SU(1,1) to those of the discrete series is calculated explicitely and the existence of two setsΦ is demonstrated.     

Two-loop divergences of field theories with nonlinear symmetry

A general formula is obtained for two-loop counterterms of the field theories with the nonlinear realization of symmetry group.