A geometrical theorem on the asymptotic space-time properties of conservation laws in a classical field theory

A simple way to construct models with early cosmological Genesis epoch is to employ bosonic fields whose Lagrangians transform homogeneously under scaling transformation. We show that in these theories, for a range of parameters defining the Lagrangian, there exists a homogeneous power-law solution in flat space-time, whose energy density vanishes, while pressure is negative (power-law Genesis). We find the condition for the legitimacy of the classical field theory description of such a situation. We note that this condition does not hold for our earlier Genesis model with vector field. We construct another model with vector field and power-law background solution in flat space-time, which is legitimately treated within classical field theory, violates the Null Energy Condition (NEC) and is stable. Upon turning on gravity, this model describes the early Genesis stage.

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SYMMETRIES IN CLASSICAL FIELD THEORY

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887804000290 ◽

2004 ◽

Vol 01 (05) ◽

pp. 651-710 ◽

Cited By ~ 23

Author(s):

MANUEL DE LEÓN ◽

DAVID MARTÍN DE DIEGO ◽

AITOR SANTAMARÍA-MERINO

Keyword(s):

Field Theory ◽

Conservation Laws ◽

Classical Field Theory ◽

Cauchy Data ◽

Classical Field ◽

Field Theories ◽

Classical Field Theories

The multisymplectic description of Classical Field Theories is revisited, including its relation with the presymplectic formalism on the space of Cauchy data. Both descriptions allow us to give a complete scheme of classification of infinitesimal symmetries, and to obtain the corresponding conservation laws.

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On the geometric structure of classical field theory in Lagrangian formulation

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100046284 ◽

1970 ◽

Vol 68 (2) ◽

pp. 475-484 ◽

Cited By ~ 31

Author(s):

Jędrzej Śniatycki

Keyword(s):

Field Theory ◽

Conservation Laws ◽

Geometric Structure ◽

Classical Field Theory ◽

Higher Order ◽

Classical Field ◽

Lagrangian Formulation ◽

Symmetry Transformations

AbstractGeometric structure of classical field theory in Lagrangian formulation is investigated. Symmetry transformations with generators depending on higher-order derivatives are considered and the corresponding conservation laws are obtained.

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