Semi-classical methods
“Classical mechanics is the model for all physical sciences”
-- M.C. Gutzwiller
Semiclassical methods provide a powerful approach to investigate the dynamics of quantum field theory. In particular, as shown in the classical series of papers by Dashen-Hasslacher-Neveu and Goldstone-Jackiw, it is possible to find solutions of the full non-linear interacting classical equations of motion of various models, which behave as stable field configurations in space-time, with particle properties. The accuracy of the approximation depends both on how much
we know about the classical problem and the strenght of the coupling constant.
The appealing feature of this approach is that it does not rely on integrable properties of the theory under scrutiny and therefore it can be used both as complementary or alternative method to the Form Factor Perturbation Theory for studying non-integrable models.
In recent years, we have investigated in several papers different properties of (1+1) dimensional Quantum Field Theory with kink excitation. In particular we have studied the finite-size scaling functions, the false vacuum decay and the general nature of the bound states. We have also studied the semi-classical spectrum of bound states of Majorana fermions. Moreover, the
prediction about the bound states of the
kinks in the Landau-Ginzburg theories has
been confirmed by a Truncated Conformal
Space Approach.
(click on the movie to see or to stop the motion of two kinks)
Relevant Publications
• G. Mussardo, Bound States of Majorana Fermions in Semiclassical Approximation JSTAT 2015 n. 12, P12003.
• A. Coser, M. Beria, G. Brandino, R. Konik, G. Mussardo, Truncated Conformal Space Approach for 2D Landau-Ginzburg Theories, JSTAT 2014 n. 12, P12010.
• G. Mussardo, Neutral Bound States in Kink-like Theories, Nucl.Phys.B779:101-154,2007, hep-th/0607025
• G. Mussardo, V. Riva, G. Sotkov, G. Delfino, Kink scaling functions in 2-D non-integrable quantum field theories, Nucl.Phys.B736:259-287,2006, hep-th/0510102
• G. Mussardo, V. Riva, G. Sotkov, Semiclassical energy levels of Sine-Gordon model with Dirichlet boundary conditions, Nucl.Phys.B705:548-563,2005, hep-th/0406246
• G. Mussardo, V. Riva, G. Sotkov, Semiclassical scaling functions of Sine-Gordon model, Nucl.Phys.B699:545-574,2004, hep-th/0405139
• G. Mussardo, V. Riva, G. Sotkov, Finite volume form-factirs in semiclassical approximation, Nucl.Phys.B670:464-478,2003, hep-th/0307125
Main References
• R.F. Dashen, B. Hasslacher, A. Neveu
Nonperturbative Methods and Extended Hadron Models in Field Theory. 1. Semiclassical Functional Methods, ,Phys.Rev.D10:4114,1974.
• R.F. Dashen, B. Hasslacher, A. Neveu
Nonperturbative Methods and Extended Hadron Models in Field Theory. 2. Two-Dimensional Models and Extended Hadrons, Phys.Rev.D10:4130-4138,1974.
• R.F. Dashen, B. Hasslacher, A. Neveu
Nonperturbative Methods and Extended Hadron Models in Field Theory. 3. Four-Dimensional Nonabelian Models, Phys.Rev.D10:4138,1974.
• J. Goldstone, R. Jackiw, Quantization of non-linear waves, Phys. Rev. D 11 (1976), 1486
• R. Rajaraman, Solitons and Instantons, North Holland (Amsterdam) 1982.