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Gut and Cosmology
Published in K Grotz, H V Klapdor, S S Wilson, The Weak Interaction in Nuclear, Particle and Astrophysics, 2020
K Grotz, H V Klapdor, S S Wilson
Before we discuss the solution of the aforementioned cosmological problems in the inflationary universe, we consider firstly the possible causes of this type of exponential behaviour. In Chapter 4 we discussed the mechanism of spontaneous symmetry breaking by means of Higgs fields. In the phase of broken symmetry these hypothetical Higgs fields have finite vacuum expectation values and associated non-zero energy densities V(Φmin)4. Higgs fields are thus good candidates for the generation of large vacuum energy densities ρv. However the standard Higgs potential V(Φ) of Chapter 4 is always negative for 0 ≤ |⟨Φ⟩| ≲ v. The vacuum energy density ρV = V(Φmin) would thus have the wrong sign to generate an exponential expansion.
The Basic Formalism of Field Theory
Published in A.N. Vasiliev, Patricia A. Millard, Functional Methods in Quantum Field Theory and Statistical Physics, 2019
A.N. Vasiliev, Patricia A. Millard
The above discussion does not pertain to the so-called anomalous situation in which spontaneous symmetry breaking occurs. In our language this phenomenon arises because the equation LL′G = 0 is not true in spite of the fact that the Schwinger equation L′G = 0 is satisfied. This is possible, roughly speaking, when the contraction of the operator L with L′G gives rise to divergences, and this “extra infinity” cancels the “zero” of L′G. The usual mechanism for the appearance of such an infinity is Goldstone particles (see Chap. 6).
Electromagnetism and Quantum Field Theory
Published in Harish Parthasarathy, Advanced Probability and Statistics: Applications to Physics and Engineering, 2023
This formula means that (tnmφ0m)n is an eigenstate of the mass matrix having zero eigenvalues. Thus, spontaneous symmetry breaking which occurs when the physics is viewed from the ground state leads to the generation of massless particles, called massless Goldstone Bosons.
Observation of string defects in liquid crystal
Published in Liquid Crystals, 2021
Kirandeep Kaur Matharu, Samriti Khosla, Sapna Sethi, Nitin Sood
Phase transitions associated with change of symmetry are described through Spontaneous symmetry breaking [14]. In this case the higher symmetry phase (less ordered) is associated with a unique true vacuum whereas in the ordered phase, the vacuum has degenerated structure and the system can choose any one of the degenerate vacua randomly after the phase transition. Consequently, a set of minimum energy configurations forms which represent vacuum manifold (M). For topological excitations manifold defines the order parameter [11]. The topology of ‘M’ represents the kind of defect to be formed while approaching the more ordered state [6,7]. These defects are represented by different homotopy groups ᴨn(M). The homotopy groups characterise mapping from the n-sphere Sn enclosing the topological excitation in real space into the vacuum manifold M [11]. In general, πn (Mo) gives the number of topologically distinct noncontractible n-spheres and π1(Mo) gives the number of topologically distinct noncontractible loops. Strings occur in theories with nontrivial π1(Mo) [2,6,7].
Symmetry and asymmetry induced dynamics in a memristive twin-T circuit
Published in International Journal of Electronics, 2022
Léandre Kamdjeu Kengne, Justin Roger Mboupda Pone, Hilaire Bertrand Fotsin
First of all, a clear distinction should be made between explicit and spontaneous symmetry breaking. Explicit symmetry breaking arises when the law governing its behaviour is changed and is no longer invariant; and spontaneous symmetry breaking occurs when the underlying laws are invariant under the symmetry but the particular realisation of the observed system is not. This latter case corresponds, for example, of solutions that appear in pairs of asymmetric attractors in various symmetric models (Kingni et al., 2019; Leutcho et al., 2018; Njitacke & Kengne, 2018; Pone et al., 2019; Tabekoueng Njitacke et al.).