|
|
| Line 1: |
Line 1: |
| {{Distinguish|Thirring model}}
| | Hello, dear friend! My name is Lidia. I smile that I could unite to the entire world. I live in United Kingdom, in the region. I dream to visit the various countries, to obtain acquainted with appealing people.<br><br>Here is my site; [http://www.cup.sod-hamburg.com/index.php?mod=users&action=view&id=103170 Biking for modern life mountain bike sizing.] |
| The '''Thirring–Wess model''' or '''Vector Meson model'''
| |
| is an exactly solvable | |
| quantum field theory describing the interaction of a [[fermion field#Dirac fields|Dirac field]] with a vector field in dimension two.
| |
| | |
| ==Definition==
| |
| The [[Lagrangian density]] is made of three terms:
| |
| | |
| the free vector field <math> A^\mu</math> is described by | |
| | |
| :<math>
| |
| {(F^{\mu\nu})^2 \over 4}
| |
| +{\mu^2\over 2} (A^\mu)^2
| |
| </math>
| |
| | |
| for <math> F^{\mu\nu}= \partial^\mu A^\nu - \partial^\nu A^\mu </math> and the boson mass <math>\mu</math> must be
| |
| strictly positive;
| |
| the free fermion field <math> \psi </math>
| |
| is described by
| |
| | |
| :<math>
| |
| \overline{\psi}(i\partial\!\!\!/-m)\psi
| |
| </math>
| |
| | |
| where the fermion mass <math>m</math> can be positive or zero.
| |
| And the interaction term is
| |
| :<math>
| |
| qA^\mu(\bar\psi\gamma^\mu\psi)
| |
| </math>
| |
| | |
| Although not required to define the massive vector field, there can be also a gauge-fixing term
| |
| :<math>
| |
| {\alpha\over 2} (\partial^\mu A^\mu)^2
| |
| </math>
| |
| for <math> \alpha \ge 0 </math>
| |
| | |
| There is a remarkable difference between the case <math> \alpha > 0 </math> and the case <math> \alpha = 0 </math>: the latter requires a [[renormalization|field renormalization]] to absorb divergences of the two point correlation.
| |
| | |
| ==History==
| |
| This model was introduced by Thirring and Wess as a version of the [[Schwinger model]] with a vector mass term in the Lagrangian .
| |
| | |
| When the fermion is massless (<math> m= 0 </math>), the model is exactly solvable. One solution was found, for <math> \alpha =1 </math>, by Thirring and Wess <ref name = tw>{{Cite journal| last = Thirring| first = W| coauthor= Wess J|
| |
| authorlink = |
| |
| title = Solution of a field theoretical model in one space one time dimensions |
| |
| journal = [[Annals Phys.]]|
| |
| volume = 27 | issue = | pages = 331–337
| |
| | year = 1964| publisher =
| |
| | url =
| |
| | format = | id = | accessdate = }}</ref>
| |
| using a method introduced by Johnson for the [[Thirring model]]; and, for <math> \alpha = 0 </math>, two different solutions were given by Brown<ref name = br>{{Cite journal| last = Brown| first = L|
| |
| authorlink = |
| |
| title = Gauge invariance and Mass in a Two-Dimensional Model|
| |
| journal = [[N.Cimento.]]|
| |
| volume = 29 | issue = | pages =
| |
| | year = 1963| publisher =
| |
| | url =
| |
| | format = | id = | accessdate = }}</ref> and Sommerfield.<ref name = sm>{{Cite journal| last = Sommerfield | first = C|
| |
| authorlink = |
| |
| title = |
| |
| journal = [[Annals Phys.]]|
| |
| volume = 26 | issue = | pages =
| |
| | year = 1964| publisher =
| |
| | url =
| |
| | format = | id = | accessdate = }}</ref> Subsequently Hagen <ref name = ha>{{Cite journal| last = Hagen| first = C|
| |
| authorlink = |
| |
| title = Current definition and mass renormalization in a Model Field Theory|
| |
| journal = [[N. Cimento A]]|
| |
| volume = 51 | issue = | pages =
| |
| | year = 1967| publisher =
| |
| | url =
| |
| | format = | id = | accessdate = }}</ref> showed (for <math> \alpha = 0 </math>, but it turns out to be true for <math> \alpha \ge 0 </math>) that there is a one parameter family of solutions.
| |
| | |
| ==References==
| |
| <references/>
| |
| | |
| ==External links==
| |
| | |
| {{Quantum field theories}}
| |
| | |
| {{DEFAULTSORT:Thirring-Wess Model}}
| |
| [[Category:Quantum field theory]]
| |
| [[Category:Exactly solvable models]]
| |
| | |
| | |
| {{Quantum-stub}}
| |
Hello, dear friend! My name is Lidia. I smile that I could unite to the entire world. I live in United Kingdom, in the region. I dream to visit the various countries, to obtain acquainted with appealing people.
Here is my site; Biking for modern life mountain bike sizing.