Hamiltonian formulation of string theory and multiloop amplitudes in the operator context

1990 ◽  
pp. 148-162
Author(s):  
Adrian R. Lugo ◽  
Jorge G. Russo
Keyword(s):  
String Theory ◽  
Hamiltonian Formulation

scholarly journals ON THE SYMMETRIES OF HAMILTONIAN SYSTEMS

1995 ◽  
Vol 10 (04) ◽  
pp. 579-610 ◽  
Author(s):  
V. MUKHANOV ◽  
A. WIPF
Keyword(s):  
String Theory ◽  
Hamiltonian Systems ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Linear Constraints ◽  
Lagrangian System ◽  
Lagrangian Systems ◽  
Diffeomorphism Invariance ◽  
Symmetry Transformations ◽  
Local Symmetries

In this paper we show how the well-known local symmetries of Lagrangian systems, and in particular the diffeomorphism invariance, emerge in the Hamiltonian formulation. We show that only the constraints which are linear in the momenta generate transformations which correspond to symmetries of the corresponding Lagrangian system. The non-linear constraints (which we have, for instance, in gravity, supergravity and string theory) generate the dynamics of the corresponding Lagrangian system. Only in a very special combination with "trivial" transformations proportional to the equations of motion do they lead to symmetry transformations. We show the importance of these special "trivial" transformations for the interconnection theorems which relate the symmetries of a system with its dynamics. We prove these theorems for general Hamiltonian systems. We apply the developed formalism to concrete physically relevant systems, in particular those which are diffeomorphism-invariant. The connection between the parameters of the symmetry transformations in the Hamiltonian and Lagrangian formalisms is found. The possible applications of our results are discussed.

A Mathematical Introduction to String Theory

1997 ◽  
Author(s):  
Sergio Albeverio ◽  
Jurgen Jost ◽  
Sylvie Paycha ◽  
Sergio Scarlatti
Keyword(s):  
String Theory

String Theory

1998 ◽  
Author(s):  
Joseph Polchinski
Keyword(s):  
String Theory

String theory tackles strange metals

Nature ◽  
2010 ◽  
Author(s):  
Eugenie Samuel Reich
Keyword(s):  
String Theory

QCD and String Theory

2007 ◽  
Author(s):  
Johanna Erdmenger
Keyword(s):  
String Theory

String theory: what is it?

1992 ◽  
Vol 162 (8) ◽  
pp. 83 ◽  
Author(s):  
A.Yu. Morozov
Keyword(s):  
String Theory

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

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