Nonperturbative Spontaneous Symmetry Breaking

A nonperturbative approach for spontaneous symmetry breaking is proposed. It is based on some conjectural properties of interacting field operators. As the consequences an additional terms like to m ² A ² appears in the initial Lagrangian.     

Symmetry Breaking for Black-Scholes Equations

Black-Scholes equation is used to model stock option pricing. In this paper, optimal systems with one to four parameters of Lie point symmetries for Black-Scholes equation and its extension are obtained. Their symmetry breaking interaction associated with the optimal systems is also studied. As a result, symmetry reductions and corresponding solutions for the resulting equations are obtained.     

Proof of Chiral Symmetry Breaking and Persistent Mass Condition in Vector- Like Gauge Theory

We give the details of rigorous proof of some mass inequalitiee in a vector-like gauge theory based on any simple group G. These mass inequalitiee lead to the conclusions that in auch a theory the chiral symmetries associated with all G representations of quarks must be spontaneously broken, and the persistent mass condition ie justified for any composite particles when the vacuum angle is zero or massless quarks exist.     

Circular Photocurrent in Weyl Semimetals with Mirror Symmetry

Journal of Experimental and Theoretical Physics - We have considered theoretically Weyl’s semimetals, for which the point symmetry group contains reflection planes and which have equivalent...     

Fano Resonance by Symmetry Breaking Stub in a Metal-Dielectric-Metal Waveguide

The coupling of a stub obliquely intersected with a metal-dielectric-metal plasmonic waveguide is investigated by using the finite difference in time domain method. Results show that an odd mode, except for the usual even mode, is excited in the stub due to the symmetry breaking of the oblique intersection. Moreover, the results show that tile quality factor of the odd mode is very high in comparison with that of the usual even mode, which is then explained by the symmetry breaking of the oblique stub intersection. The superposition of the even and the odd mode generates a Fano shaped spectrum with a very narrow linewidth. The effect of metallic loss and compensation are also discussed. Both the stub and the waveguide are compact in size, and simple in structure, which are beneficial for the achievements of narrow band filtering, sensing, lasing, and nonlinearity enhancement.     

Discrete Symmetry Breaking for Certain Short-Range Interactions

Georgii's theorem ensures that, restricted to two-dimensional planes, a single ocean (i.e., infinite connected component) of a ground state and islands (i.e., finite connected components) are observed in lattice spin systems at sufficiently low temperature. This paper extends his results for higher dimensional hyperplanes. Our proof is mainly based on a kind of Peierls argument and is different from Georgii's, which relies on the percolation method.     

Fermion Determinant with Dynamical Chiral Symmetry Breaking

One-loop fermion determinant is discussed for the case in which the dynamical chiral symmetry breakingcaused by momentum-dependent fermion self-energy ∑(p2) takes place. The obtained series generalizes the heat kernelexpansion for hard fermion mass.     

Insight into Phenomena of Symmetry Breaking Bifurcation

We show that symmetry-breaking (SB) bifurcation is just a transition of different forms of symmetry, while still preserving system's symmetry. SB bifurcation always associates with a periodic saddle-node bifurcation, identifiable by a zero maximum of the top Lyapunov exponent of the system. In addition, we show a significant phase portrait of a newly born periodic saddle and its stable and unstable invariant manifolds, together with their neighbouring flow pattern of Poincaré mapping points just after the periodic saddle-node bifurcation, thus gaining an insight into the mechanism of SB bifurcation.     

Exactly Solvable Models and Spontaneous Symmetry Breaking

We study a few two-dimensional models with massless and massive fermions in the hamiltonian framework and in both conventional and light-front (LF) forms of field theory. The new ingredient is a modification of the canonical procedure by taking into account solutions of the operator field equations. After summarizing the main results for the derivative-coupling and the Thirring models, we briefly compare conventional and LF versions of the Federbush model including the massive current bosonization and a Bogoliubov transformation to diagonalize the Hamiltonian. Then we sketch an extension of our hamiltonian approach to the two-dimensional Nambu–Jona-Lasinio model and the Thirring-Wess model. Finally, we discuss the Schwinger model in a covariant gauge. In particular, we point out that the solution due to Lowenstein and Swieca implies the physical vacuum in terms of a coherent state of massive scalar field and suggest a new formulation of the model’s vacuum degeneracy.     

Biased Motion in a Symmetric Periodic Potential by Breaking Temporal Symmetry

Unidirectional transport of a particle in a spatially periodic and symmetric potential under a periodic force with broken temporal symmetry is studied.With a collaboration of the potential field and the asymmetric ac force,a dc current can be observed.Resonant current steps are found for a finite period of the ac force.A phase diagram of these resonant steps is given.Stochastic-resonance-like directional transport induced by thermal nonises is revealed.     

Fermion Determinant with Dynamical Chiral Symmetry Breaking

One-loop fermion determinant is discussed for the case in which the dynamical chiral symmetry breaking caused by momentum-dependent fermion self-energy Σ(p²) takes place. The obtained series generalizes the heat kernel expansion for hard fermion mass.     

Emergence,Singularities, and Symmetry Breaking

This paper looks at emergence in physical theories and argues that an appropriate way to understand socalled “emergent protectorates” is via the explanatory apparatus of the renormalization group. It is argued that mathematical singularities play a crucial role in our understanding of at least some well-defined emergent features of the world.     

First-Order Symmetry Energy Induced by Neutron-Proton Mass Difference

The lst-order symmetry energy coefficient of nuclear matter induced merely by the neutron-proton(h-pj mass difference is derived analytically,which turns out to be completely model-independent.Based on this result,the lst-order symmetry energy E_(sym,1)~((npDM))(A) of heavy nuclei such as ~(208)Pb induced by the n-p mass difference is investigated with the help of a local density approximation combined with the Skyrme energy density functionals.Although E_(sym,1)~((npDM))(A) is small compared with the second-order symmetry energy,it cannot be dropped simply for an accurate estimation of nuclear masses as it is still larger than the rms deviation given by some accurate mass formulas.It is therefore suggested that one perhaps needs to distinguish the neutron mass from the proton one in the construction of nuclear density functionals.     

Symmetry Breaking Due to Conformally Invariant Scalar Field

In the framework of Weyl invariant gravitational field theory including torsion coupled to a scalar field with arbitrary selfinteraction it will be shown that any solution of such a generalized Goldstone model contains the conformally invariant field of a massless scalar particle. Due to this fact it may happen that dynamical symmetry breaking becomes impossible.     

Spontaneous Electro-Weak Symmetry Breaking and Cold Dark Matter

In the standard model, the weak gauge bosons and fermions obtain mass after spontaneous electro-weak symmetry breaking, which is realized by one fundamental scalar field, namely the Higgs field. We study the simplest scalar cold dark matter model in which the scalar cold dark matter also obtains mass by interaction with the weakdoublet Higgs field, in the same way as those of weak gauge bosons and fermions. Our study shows that the correct cold dark matter relic abundance within 3a uncertainty （0.093 〈 Ωdmh^2 〈 0.129） and experimentally allowed Higgs boson mass （114.4 ≤ mh≤ 208 GeV） constrain the scalar dark matter mass within 48 ≤ ms ≤ 78 GeV. This result is in excellent agreement with the result of de Boer et al. （50 ~ 100 GeV）. Such a kind of dark matter annihilation can account for the observed gamma rays excess （10σ） at EGRET for energies above 1 GeV in comparison with the expectations from conventional Galactic models. We also investigate other phenomenological consequences of this model. For example, the Higgs boson decays dominantly into scalar cold dark matter if its mass lies within 48 ~ 64 GeV.     

Quantifying Spontaneously Symmetry Breaking of Quantum Many-Body Systems

Spontaneous symmetry breaking is related to the appearance of emergent phenomena, while a non-vanishing order parameter has been viewed as the sign of turning into such symmetry-breaking phase. We study the spontaneous symmetry breaking in the conventional superconductor and Bose–Einstein condensation with a continuous measure of symmetry by showing that both the many-body systems can be mapped into the many spin model. We also formulate the underlying relation between the spontaneous symmetry breaking and the order parameter quantitatively. The degree of symmetry stays unity in the absence of the two emergent phenomena, while decreases exponentially at the appearance of the order parameter which indicates the inextricable relation between the spontaneous symmetry and the order parameter.     

Collective Directional Transport in Symmetric Periodic Potentials by Breaking the Coupling Symmetry

Collective unidirectional motion of an asymmetrically coupled array of oscillators in symmetric periodic potentials is studied. A directed current is observed when the drift coupling is presented, while no external biased force is applied. Negative directed current is found when varying system parameters. An addition of a periodic rocking force may enhance the efficiency of directed transport. Resonant steps of the current are found and interpreted as the mode locking between the array and the ac force. Noise-assisted transport is observed, and an optimal noise intensity can give rise to a most efficient transport. The directed transport thus can be optimized and furthermore controlled by suitably adjusting the parameters of the system.