Finite Temperature Field Theory and Phase Transitions *
نویسنده
چکیده
We review different aspects of field theory at zero and finite temperature, related to the theory of phase transitions. We discuss different renormalization conditions for the effective potential at zero temperature, emphasizing in particular the MS renormalization scheme. Finite temperature field theory is discussed in the real and imaginary time formalisms, showing their equivalence in simple examples. Bubble nucleation by thermal tunneling, and the subsequent development of the phase transition is described in some detail. Some attention is also devoted to the breakdown of the perturbative expansion and the infrared problem in the finite temperature field theory. Finally the application to baryogenesis at the electroweak phase transition is done in the Standard Model and in the Minimal Supersymmetric Standard Model. In all cases we have translated the condition of not washing out any previously generated baryon asymmetry by upper bounds on the Higgs mass. IEM-FT-187/99 January 1999 Based on lectures given at the Summer School in High Energy Physics and Cosmology, ICTP, Trieste (Italy) 29 June–17 July 1998. 1 The effective potential at zero temperature The effective potential for quantum field theories was originally introduced by Euler, Heisenberg and Schwinger , and applied to studies of spontaneous symmetry breaking by Goldstone, Salam, Weinberg and Jona-Lasinio. Calculations of the effective potential were initially performed at one-loop by Coleman and E. Weinberg and at higher-loop by Jackiw and Iliopoulos, Itzykson and Martin . More recently the effective potential has been the subject of a vivid investigation, especially related to its invariance under the renormalization group. I will try to review, in this section, the main ideas and update the latest developments on the effective potential. 1.1 Generating functionals To fix the ideas, let us consider the theory described by a scalar field φ with a lagrangian density L{φ(x)} and an action S[φ] = ∫ dxL{φ(x)} (1) The generating functional (vacuum-to-vacuum amplitude) is given by the pathintegral representation, Z[j] = 〈0out | 0in〉j ≡ ∫ dφ exp{i(S[φ] + φj)} (2) where we are using the notation φj ≡ ∫ dxφ(x)j(x) (3) Using (2) one can obtain the connected generating functional W [j] defined as, Z[j] ≡ exp{iW [j]} (4) and the effective action Γ[φ] as the Legendre transform of (4) Γ[φ] = W [j]− ∫ dx δW [j] δj(x) j(x) (5) where φ(x) = δW [j] δj(x) (6)
منابع مشابه
Magnetic Properties and Phase Transitions in a Spin-1 Random Transverse Ising Model on Simple Cubic Lattice
Within the effective-field theory with correlations (EFT), a transverse random field spin-1 Ising model on the simple cubic (z=6) lattice is studied. The phase diagrams, the behavior of critical points, transverse magnetization, internal energy, magnetic specific heat are obtained numerically and discussed for different values of p the concentration of the random transverse field.
متن کاملQuantum Field Theory at Finite Temperature: an Introduction
In these notes we review some properties of Statistical Quantum Field Theory at equilibrium, i.e Quantum Field Theory at finite temperature. We explain the relation between finite temperature quantum field theory in (d, 1) dimensions and statistical classical field theory in d + 1 dimensions. This identification allows to analyze the finite temperature QFT in terms of the renormalization group ...
متن کاملFirst order phase transitions in a Bianchi type-I universe
Considering the theory of induced gravity coupled to matter fields, taking the φ6 interaction potential model we evaluate the one-loop effective potential in a (3+1)dimensional Bianchi type-I spacetime. It is proved that the φ6 theory can be regularised in (3+1)dimensional curved spacetime. We evaluate the finite temperature effective potential and study the temperature dependence of phase tran...
متن کاملSuperconducting Phase Transitions in 2+1 Dimensional Quantum Field Theories Modeling Generalized Polaronic Interactions I: Jahn-teller Inspired Models
We review the fundamentals of Jahn-Teller interactions and their field theoretical modelings and show that a 2+1 dimensional gauge theory where the gauge field couples to “flavored fermions” arises in a natural way from a two-band model describing the dynamical Jahn-Teller effect. The theory exhibits a second order phase transition to novel finite-temperature superconductivity.
متن کاملMetallic spin glasses
Recent work on the zero temperature phases and phase transitions of strongly random electronic system is reviewed. The transition between the spin glass and quantum paramagnet is examined, for both metallic and insulating systems. Insight gained from the solution of infinite range models leads to a quantum field theory for the transition between a metallic quantum paramagnetic and a metallic sp...
متن کاملMott transitions in two-orbital Hubbard systems
We investigate the Mott transitions in two-orbital Hubbard systems. Applying the dynamical mean field theory and the self-energy functional approach, we discuss the stability of itinerant quasi-particle states in each band. It is shown that separate Mott transitions occur at different Coulomb interaction strengths in general. On the other hand, if some special conditions are satisfied for the i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008