CANONICAL CONNECTIONS IN GAUGE-NATURAL FIELD THEORIES

2008 ◽  
Vol 05 (06) ◽  
pp. 973-988 ◽  
Author(s):  
MARCO FERRARIS ◽  
MAURO FRANCAVIGLIA ◽  
MARCELLA PALESE ◽  
EKKEHART WINTERROTH
Keyword(s):  
Phase Space ◽  
Global Existence ◽  
Conservation Laws ◽  
Field Theories ◽  
Hamiltonian Form ◽  
Natural Field ◽  
Spinor Connection ◽  
Fermionic Fields ◽  
Conserved Current ◽  
A Current

We investigate canonical aspects concerning the relation between symmetries and conservation laws in gauge-natural field theories. In particular, we find that a canonical spinor connection can be selected by the simple requirement of the global existence of canonical superpotentials for the Lagrangian describing the coupling of gravitational and Fermionic fields. In fact, the naturality of a suitably defined variational Lagragian implies the existence of an associated energy-momentum conserved current. Such a current defines a Hamiltonian form in the corresponding phase space; we show that an associated Hamiltonian connection is canonically defined along the kernel of the generalized gauge-natural Jacobi morphism and uniquely characterizes the canonical spinor connection.

Perturbations of conservation laws in field theories

1986 ◽  
Vol 167 (2) ◽  
pp. 354-389 ◽  
Author(s):  
Judith M Arms ◽  
Ian M Anderson
Keyword(s):  
Conservation Laws ◽  
Field Theories

Conformal Field Theory of Free Bosonic and Fermionic Fields

2020 ◽  
pp. 443-475
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theories ◽  
Majorana Fermion ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Bosonic Field ◽  
Conformal Field ◽  
Mathematical Identities ◽  
Modular Transformations ◽  
Fermionic Fields ◽  
The Subject

Free theories are usually regarded as trivial examples of quantum systems. This chapter proves that this is not the case of the conformal field theories associated to the free bosonic and fermionic fields. The subject is not only full of beautiful mathematical identities but is also the source of deep physical concepts with far reaching applications. Chapter 12 also covers quantization of the bosonic field, vertex operators, the free bosonic field on a torus, modular transformations, the quantization of the free Majorana fermion, the Neveu–Schwarz and Ramond sectors, fermions on a torus, calculus for anti-commuting quantities and partition functions.

Structures of conserved currents and mass spectra for scalar fields: an approach to the generalization of the Goldstone theorem

1980 ◽  
Vol 58 (4) ◽  
pp. 463-471
Author(s):  
Meiun Shintani
Keyword(s):  
Mass Spectrum ◽  
Scalar Field ◽  
Mass Spectra ◽  
Vacuum State ◽  
Scalar Fields ◽  
Goldstone Theorem ◽  
Massive Mode ◽  
Conserved Current ◽  
Conserved Currents ◽  
A Current

Considering the commutators between a scalar field and a conserved current, we shall clarify the connection between the mass spectrum for a scalar field and the structures of a current. For a special form of currents involving c-number functions, non-invariance of the vacuum under the corresponding transformation entails the existence of a massive mode. It is shown that once a type of currents is specified, the pole structures for [Formula: see text] depend only on c-number parts of Jμ(x). We shall show that the non-vanishing Goldstone commutator does not automatically imply the degeneracy of the vacuum state, and discuss the applicability of the Goldstone theorem.

scholarly journals A study of the nature of the field theories of the electron and positron and of the meson

1946 ◽  
Vol 185 (1000) ◽  
pp. 14-34 ◽  
Keyword(s):  
Current Density ◽  
Magnetic Moment ◽  
Poynting Vector ◽  
Field Theories ◽  
Meson Field ◽  
Theory Of Relativity ◽  
Magnetic Current ◽  
Additional Degree ◽  
Additional Dimension ◽  
A Current

The field theories of the electron and positron and also of the meson are developed by means of a close analogy with the photon. The analogy consists in the representation of the tracks of these particles by means of null-geodesics. The choice of notation is guided by the attempt to arrive at a theory in which the lengths (h/m 0 c) and (e 2 /m 0 c 2 ) occur naturally without reference to the structure of the particles, and in which the concept of quantization of electric charge is included. It is found that these objects can be attained by assuming that an additional degree of freedom is necessary for the description of the particles. If this is regarded as an additional dimension, it is found that an exact analogy can be made with the field theories familiar in the theory of relativity. An important feature is the union, in a single tensor, of energy, momentum and current density. A certain arbitrariness, not unlike that associated with the Poynting vector, is revealed, and it is shown that if this is removed by making a definite choice of the magnitude of the magnetic moment of the electron and positron, the spin angular momefttum is ^hereby fixed at the value 1/2h. In the development of the meson field the analogy shows* that the nuclear sources of the field act as if contributing a current density analogous to a magnetic current density in the electromagnetic case. The use of the additional degreb of freedom in the sinusoidal form indicates that the ratio of the constants g 1 and g 2 introduced into field theories as measures of the strengths of the sources is determined by the mass of the particle emitted in the neutron-proton transition.

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