Dynamical symmetry breaking in Yang–Mills geometrodynamics

In this paper, we want to better understand the causality reflection that arises under a subset of Abelian local gauge transformations in geometrodynamics. We proved in previous papers that in Einstein–Maxwell spacetimes, there exist two local orthogonal planes of gauge symmetry at every spacetime point for non-null electromagnetic fields. Every vector in these planes is an eigenvector of the Einstein–Maxwell stress–energy tensor. The vectors that span these local orthogonal planes are dependent on electromagnetic gauge. The local group of Abelian electromagnetic gauge transformations has been proved isomorphic to the local groups of tetrad transformations in these planes. We called LB1 the local group of tetrad transformations made up of SO(1, 1) plus two different kinds of discrete transformations. One of the discrete transformations is the full inversion two by two which is a Lorentz transformation. The other discrete transformation is given by a matrix with zeroes on the diagonal and ones off-diagonal two by two, a reflection. The group LB1 is realized on this plane, we call this plane one, and is spanned by the time-like and one space-like vectors. The other local orthogonal plane is plane two and the local group of tetrad transformations, we call this LB2, which is just SO(2). The local group of Abelian electromagnetic gauge transformations is isomorphic to both LB1 and LB2, independently. It has already been proved that a subset of local electromagnetic gauge transformations that leave the electromagnetic tensor invariant induces a change in sign in the norm of the tetrad vectors that span the local plane one. The reason is that one of the discrete transformations on the local plane one that belongs to the group LB1 is not a Lorentz transformation, it is a flip or reflection. It is precisely on this kind of discrete transformation that we have an interest since it has the effect of changing the signature and the causality. This effect has never been noticed before.

The Landau-Khalatnikov-Fradkin transformations (LKFTs) allow to interpolate $n$-point functions between different gauges. We first offer an alternative derivation of these LKFTs for the gauge and fermions field in the Abelian (QED) case when working in the class of linear covariant gauges. Our derivation is based on the introduction of a gauge invariant transversal gauge field, which allows a natural generalization to the non-Abelian (QCD) case of the LKFTs. To our knowledge, within this rigorous formalism, this is the first construction of the LKFTs beyond QED. The renormalizability of our setup is guaranteed to all orders. We also offer a direct path integral derivation in the non-Abelian case, finding full consistency.

Duality equivalence between self-dual and topologically massive non-abelian models

In this Ph.D. thesis, accepted at the Vrije Universiteit Brussel, we review and elaborate on a method to find the D‐brane effective action, based on BPS equations. Firstly, both for the Yang‐Mills action and the Born‐Infeld action it is shown that these configurations are indeed BPS, i.e. solutions to these equations saturate a Bogomolny bound and leave some supersymmetry unbroken. Next, we use the BPS equations as a tool to construct the D‐brane effective action and require that (a deformation of) these equations should still imply the equations of motion in more general cases. In the abelian case we managed to calculate all order in α′ four‐derivative corrections to the effective action and the BPS equations while in the non‐abelian case we obtained the effective action up to order α′4. Furthermore, we discuss a check based on the spectrum of strings stretching between intersecting branes. Finally, this Ph.D. thesis also discusses the construction of a boundary superspace which would be the first step to use the method of Weyl invariance in N = 2 superspace in order to again construct the D‐brane effective action. A more detailed summary of each section can be found in the introduction.

Internal symmetry in protein structures: prevalence, functional relevance and evolution

Gauge independence as a consequence of gauge covariance

It is shown how vector Stueckelberg fields can be introduced to ensure gauge invariance for mass terms for an antisymmetric tensor field. Scalar Stueckelberg fields allow one to have gauge invariance for these vector fields. Both the Abelian and non-Abelian cases are considered. Fully antisymmetric rank-three tensor fields and symmetric rank-two tensor fields are also discussed. PACS No.: 11.15-1

This paper aims at treating a study on Sylow theorem of different algebraic structures as groups, order of a group, subgroups, along with the associated notions of automorphisms group of the dihedral groups, split extensions of groups and vector spaces arises from the varying properties of real and complex numbers. We must have used the Sylow theorems of this work when it's generalized. Here we discuss possible subgroups of a group in different types of order which will give us a practical knowledge to see the applications of the Sylow theorems. In algebraic structures, we deal with operations of addition and multiplication and in order structures, those of greater than, less than and so on. It is through the study of Sylow theorems that we realize the importance of some definitions as like as the exact sequences and split extensions of groups, Sylow p-subgroup and semi-direct product. Thus it has been found necessary and convenient to study these structures in detail. In situations, where it was found that a given situation satisfies the basic axioms of structure and having already known the properties of that structure. Finally, we find out possible subgroups of a group in different types of order for abelian and non-abelian cases.

We develop the theory of the nonadiabatic geometric phase, in both the Abelian and non-Abelian cases, in quaternionic Hilbert space.

Spontaneous Lorentz violation realized through a nonlinear vector field constraint of the type A μ A μ = M 2 ( M is the proposed scale for Lorentz violation) is shown to generate massless vector Goldstone bosons, gauging the starting global internal symmetries in arbitrary relativistically invariant theories. The gauge invariance appears in essence as a necessary condition for these bosons not to be superfluously restricted in degrees of freedom, apart from the constraint due to which the true vacuum in a theory is chosen by the Lorentz violation. In the Abelian symmetry case the only possible theory proves to be QED with a massless vector Goldstone boson naturally associated with the photon, while the non-Abelian symmetry case results in a conventional Yang–Mills theory. These theories, both Abelian and non-Abelian, look essentially nonlinear and contain particular Lorentz (and CPT) violating couplings when expressed in terms of the pure Goldstone vector modes. However, they do not lead to physical Lorentz violation due to the simultaneously generated gauge invariance.

We construct a Lagrangian for the massive scalar multiplet, locally invariant under two types of spinorial transformations (N=2 supersymmetry). Our theory is based on the coupling of the global supermultiplet to N=2 supergravity and corrections generated iteratively in powers of Newton's constant. Consistency of the theory requires the vector field of supergravity to gauge the central charge represented in the massive sector of the multiplet. The same vector may alternatively gauge the internal 0(2) symmetry of the two supersymmetry generators. Furthermore, it may even gauge a linear combination of the generators of these two groups; we indicate the grounds for this compatibility. We discuss the hierarchy of internal symmetries characterizing each sector of the theory, ranging from U(1)xSU(2)xSU(2) down to 0(2)x0(2). This internal symmetry imposes tight constraints on the system. For instance, the nonpolynomial structure of the spinless fields at hand is considerably more restricted than that present in the general simple supersymmetric (N-1) theory. Furthermore, the vector field is forced to couple to the matter fields with gravitational strength, to the effect that the resulting Coulomb potential exactly cancels against the Newtonian potential of gravity, in the static limit. Our theory may be also viewed as a truncation of N=8 supergravity theory, compatibly with the SO (8) breakup scheme into SU(3)xU(1)xU(1). The potential of the spinless fields present has a local minimum at the origin, but further off it is not even bounded from below. However, we point out some indications that the tunneling out of the supersymmetric, metastable vacuum is negligibly small.

Many satisfiability problems exhibit symmetry properties. Thus, the development of symmetry exploitation techniques seems a natural way to try to improve the efficiency of solvers by preventing them from exploring isomorphic parts of the search space. These techniques can be classified into two categories: dynamic and static symmetry breaking. Static approaches have often appeared to be more effective than dynamic ones. But although these approaches can be considered as complementary, very few works have tried to combine them.In this paper, we present a new tool, CosySEL, that implements a composition of the static Effective Symmetry Breaking Predicates (esbp) technique with the dynamic Symmetric Explanation Learning (sel). esbp exploits symmetries to prune the search tree and sel uses symmetries to speed up the tree traversal. These two accelerations are complementary and their combination was made possible by the introduction of Local symmetries.We conduct our experiments on instances issued from the last ten sat competitions and the results show that our tool outperforms the existing tools on highly symmetrical problems.KeywordsBoolean satisfiabilitySymmetryDynamic symmetry breakingStatic symmetry breakingLocal symmetries

This review summarized the data obtained by the author in studies on internal symmetry of the mirror type in primary structures of proteins. The methods for detection of symmetric segments in amino acid sequences are analyzed: (1) the method based on analysis of sequences of roots of amino acid codons; (2) the dot matrix method; (3) the method of internal symmetry scanning. The results of studies of internal symmetry in enzymes and signaling proteins are presented. The probable role of the internal symmetry in the structural-functional organization of proteins is discussed.

We present a JWKB theory which describes the propagation of seismic surface waves in a laterally heterogeneous, anisotropic waveguide. We introduce a local dispersion relation and local vertical eigenfunctions which depend explicitly on the direction of the local wavevector as a consequence of the anisotropy. the variation of amplitude along a surface wave ray path is determined by a conservation law for the surface wave energy. Apart from the usual dynamical phase, which is the integral of the local wavevector along a ray path, there is an additional variation in phase in a general anisotropic waveguide. This additional phase, which is an analogue of the Berry phase in adiabatic quantum mechanics, vanishes in a waveguide with a local vertical two-fold symmetry axis or a local horizontal mirror plane.

We investigate the Schwinger effect for the gauge bosons in an unbroken non-Abelian gauge theory (e.g. the gluons of QCD). We consider both constant “color electric” fields and “color magnetic” fields as backgrounds. As in the Abelian Schwinger effect we find there is production of “gluons” for the color electric field, but no particle production for the color magnetic field case. Since the non-Abelian gauge bosons are massless there is no exponential suppression of particle production due to the mass of the electron/positron that one finds in the Abelian Schwinger effect. Despite the lack of an exponential suppression of the gluon production rate due to the masslessness of the gluons, we find that the critical field strength is even larger in the non-Abelian case as compared to the Abelian case. This is the result of the confinement phenomenon on QCD.