By T. Borne, G. Lochak, H. Stumpf

Provides a brand new view of quantum box concept, an entire new interpretation of nonperturbative regularization and chance, and a brand new remedy of potent dynamics of quantum fields, in accordance with algebraic illustration thought in sensible areas.

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**Additional resources for Nonperturbative Quantum Field Theory and the Structure of Matter (Fundamental Theories of Physics)**

**Sample text**

1 Fusion Concepts in Relativistic Quantum Field Theory 41 with a four-component spinor field 4 and with the coupling constant l, which was considered as a fundamental length. This equation is invariant under two chiral transformations: the Touschek transformation and the Pauli–Gürsey transformation. 1) in terms of Weyl spinors, see [Dürr 61]. 1) contains an elementary algebraic isospin degree of freedom. 2) the interaction term is strictly local in order not to violate relativistic microcausality.

In the preceding section we arrived at the conclusion that a nonlinear spinor field forms a suitable candidate for an extension of the quantum mechanical fusion conception to relativistic quantum field theory. This choice is enforced by group theory: 48 2 The Spinor Field Model the essential symmetry group of relativistic quantum fields is the Poincaré group. All representations of this group can be generated by direct products of elementary spin representations, Wigner [Wign 39], Fonda and Ghirardi [Fon 70], Bogoliubov, Logunov and Todorov [Bogo 75], Haag [Haag 92].

2) of Dürr. This reformulation was fully acknowledged by Heisenberg, see [Hei 66]. Although such an equation seems to be very fundamental, it is the source of serious difficulties; in particular, it prevents the formation of bound states as we already remarked. In 1961 Nambu and Jona–Lasinio made an attempt to remove these difficulties and proposed a nonlinear spinor field equation for massive Dirac spinors which was afterwards in different versions denoted as the NJL model (equation). We briefly describe their motivation and techniques to arrive at this result, and for simplicity we omit the isospinor part because it plays no role with respect to the arguments of Nambu and Jona–Lasinio [Nam 61a,b].

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