Goldstoneov teorem

Goldstoneov teorem igra ključno vlogo pri razumevanju spontanega zloma simetrije v kvantni teoriji polja. Na njegove posledice naletimo tudi v sistemih kondenzirane snovi, kot so superfluidi in feromagneti. Osnovna ideja teorema je preprosta: pri spontanem zlomu zvezne simetrije se v sistemu pojavijo brezmasni Goldstoneovi bozoni. V članku po kratkem pregledu definicij sledi natančnejša formulacija Goldstoneovega teorema. Predstavljena sta dva dokaza, prvi v kontekstu klasične, drugi pa kvantne teorije polja. Na koncu je navedenih nekaj primerov uporabe Goldstoneovega teorema, ki nakazujejo na potrebo po njegovih posplošitvah.

Goldstone theorem

The Goldstone theorem plays a crucial role in understanding spontaneous symmetry breaking in quantum field theory. Its implications are also found in condensed matter systems, such as superfluids and ferromagnets. The basic idea of the theorem is simple: spontaneous breaking of a continuous symmetry implies the existence of massless Goldstone bosons. In the article, after a brief review of definitions, a more precise formulation of the Goldstone theorem follows. Two proofs are presented, the first in the context of classical field theory and the second in quantum field theory. Finally, several examples of the application of the Goldstone theorem are provided, indicating the need for its generalizations.