Symmetry spontaneous breakdown

It was demonstrated by Higgs [50] that the appearance of massless bosons can be avoided by combining the spontaneous breakdown of symmetry under a compact Lie group with local gauge symmetry. The potential V() which is invariant under the local transformation of the charged field... 

The Lagrangian formulation is equally effective for discussing the idea of spontaneous breakdown of symmetry and the effect thereof can be demonstrated in terms of a simple example [18, 19]. 

Spontaneous breakdown of acetals is an example of the SnI type of reaction, uni-molecular elimination from a tetrahedral center. Reaction pathways for this general type of reaction have been derived by analysis of deviations from the expected symmetry of tetrahedral molecules of the YMX3 and MX4 formulation [95]. 

There is a number of ways to violate a symmetry. The most naive way is to violate such a symmetry directly. For example, the masses of fhe up and down quarks, mu and md violate a chiral symmetry of QCD. That is the most natural way for classical physics. In the case of quantum field theory, such a violation for the relativity and related effects can most likely take form of an external field (see Section 4 below). In particular, the spontaneous breakdown of symmetries takes the form of certain external fields. 

ABSTRACT We present a dynamical scheme for biological systems. We use methods and techniques of quantum field theory since our analysis is at a microscopic molecular level. Davydov solitons on biomolecular chains and coherent electric dipole waves are described as collective dynamical modes. Electric polarization waves predicted by Frohlich are identified with the Goldstone massless modes of the theory with spontaneous breakdown of the dipole-rotational symmetry. Self-organization, dissipativity, and stability of biological systems appear as observable manifestations of the microscopic quantum dynamics. 

Where the vacuum does not exhibit the same invariance of the Lagrangian, one says that a spontaneous breakdown of the symmetry occurs. General theorems have been derived which elucidate the dynamical consequences on the whole system of the interplay between a symmetric Lagrangian and a nonsymmetric vacuum. The Goldstone theorem is a... 

The parameter e has to be put to zero only after all the mathematical manipulations have been performed. Equation (3.46) is referred to as the spontaneous breakdown of the SC/(2) dipole rotational symmetry. 

C. De Concini and G. Vitiello, Spontaneous Breakdown of Symmetry and Group Contractions, Nucl Phys. 116B, 141-156 (1976). C. De Concini and G. Vitiello, Relation Between Projective Geometry and Group Contraction in Spontaneously Broken Symmetries, Phys. Lett. 70B, 355-357 (1977). 

Non-adiabatic coupling is also termed vibronic coupling as the resulting breakdown of the adiabatic picture is due to coupling between the nuclear and electi onic motion. A well-known special case of vibronic coupling is the Jahn-Teller effect [14,164-168], in which a symmetrical molecule in a doubly degenerate electronic state will spontaneously distort so as to break the symmetry and remove the degeneracy. 

Higgs, P.W. (1966). Spontaneous symmetry breakdown without massless bosons, Phys. Rev. 145, 1156-1163. 

The most important consequence of the breakdown of the B-O approximation is indisputably the Jahn-Teller (J-T) effect [7], where the structure defined on the basis of this approximation does not in fact hold. The important role of the J-T effect is emphasized in Bersuker s book [8] Moreover, since the J-T effect has been shown to be the only source of spontaneous distortion of high-symmetry configurations, we come to the conclusion that the J-T effect is a unique mechanism of all the symmetry breakings in condensed matter. It is of course well known that problems related to the definition of crystallic structure in solid-state physics are mostly ignored assuming only BO structures. Nevertheless it is often criticised by scientists dedicated to studies of the J-T effect. For instance the proper understanding of superconductors should be evidently based on a solution of the non-adiabatic problem but the impact on the crystallic structure is neither reflected in the Frohlich Hamiltonian [9,10] nor in the BCS theory [11]. 

The spontaneous electric polarization is a vector and represents a breakdown of symmetry that is, there is a directional preference. If the liquid crystal properties are independent of the director axis h direction (i.e., +/ is the same as — ),, if it exists, must be locally perpendicular to / . In the case of smectic-A, which possesses rotational symmetry around h, p must therefore be vanishing. In the case of smectic-C, there is a reflection symmetry (mirror symmetry) about the plane defined by the h and z axes, so p is also vanishing. 

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