Ginocchio argued that chiral symmetry breaking in QCD is responsible for the relativistic pseudospin symmetry in the Dirac equation, explaining the observed approximate pseudospin symmetry in sizable nuclei. On a much smaller scale, it is known that spin-orbit splittings in hadrons are small. Specifically, new experimental data from CLEO indicate small splittings in D-mesons. For heavy-light me...

We investigate four-fermion interactions with N -component fermion in Einstein universe for arbitrary space-time dimensions (2 ≤ D < 4). It is found that the effective potential for composite operator ψψ is calculable in the leading order of the 1/N expansion. The resulting effective potential is analyzed by varying the curvature of the space-time and is found to exhibit the symmetry restoratio...

We give a brief review of the physics of spontaneous symmetry breaking. The field-theoretic Goldstone theorem and its consequences are emphasized. In relativistic quantum theory, the emergence of particle masses is connected with spontaneous breaking of chiral symmetry. While in the Standard model of the electroweak interaction this is achieved by the Higgs mechanism, we show on a simple model ...

We examine a hidden symmetry of the hydrogen atom in quantum mechanics using the quantum mechanical analog of the classical Lenz vector and its relation to the generators of the familiar SO(3) rotational group. We use as our tool some basic concepts in algebraic group theory. The result is a mathematical description of a higher-dimension symmetry under the SO(4) group, or the rotational group i...

The equivalence theorem, between the longitudinal gauge bosons and the states eaten up by them in the process of symmetry breaking, is shown to be valid in a class of models where the details of dynamical symmetry breaking makes it obscure. In a recent paper [1], Donoghue and Tandean have made an intriguing point regarding the validity of the equivalence theorem [2, 3, 4, 5, 6, 7] in a class of...

We consider SU(2)-equivariant dimensional reduction of Yang-Mills-Dirac theory on manifolds of the form M × CP , with emphasis on the effects of non-trivial magnetic flux on CP . The reduction of Yang-Mills fields gives a chain of coupled Yang-Mills-Higgs systems on M with a Higgs potential leading to dynamical symmetry breaking, as a consequence of the monopole fields. The reduction of SU(2)-s...

The lack of deviations from the Standard Model at the current level of experimental precision can be explained systematically in suitable models of dynamical electro–weak symmetry breaking. The key ingredient is dynamics which produces a scalar unitarity partner for the Goldstone–Bosons and which leads to a decoupling of effects beyond the Standard Model. A phenomenologically successful left–ri...

We propose an approach to manipulate and control transport in Hamiltonian systems which are characterized by a mixed phase space. The approach is based on symmetry breaking of the phase space structure by applying a zero-mean periodic force for a finite duration of time. This induces time and space reversal asymmetry, which modifies the internal dynamics of the system and leads to directed tran...

Ideally an embedding of an N -dimensional dynamical system is N -dimensional. Ideally, an embedding of a dynamical system with symmetry is symmetric. Ideally, the symmetry of the embedding is the same as the symmetry of the original system. This ideal often cannot be achieved. Differential embeddings of the Lorenz system, which possesses a twofold rotation symmetry, are not ideal. While the dif...

Mechanical systems can display topological characteristics similar to that of topological insulators. Here we report a large class of topological mechanical systems related to the BDI symmetry class. These are self-assembled chains of rigid bodies with an inversion centre and no reflection planes. The particle-hole symmetry characteristic to the BDI symmetry class stems from the distinct behavi...