# GENERALIZED SCHRÖDINGER EQUATION IN EUCLIDEAN FIELD THEORY

@article{Conrady2004GENERALIZEDSE, title={GENERALIZED SCHR{\"O}DINGER EQUATION IN EUCLIDEAN FIELD THEORY}, author={Florian Conrady and Carlo Rovelli}, journal={International Journal of Modern Physics A}, year={2004}, volume={19}, pages={4037-4068} }

We investigate the idea of a "general boundary" formulation of quantum field theory in the context of the Euclidean free scalar field. We propose a precise definition for an evolution kernel that propagates the field through arbitrary space–time regions. We show that this kernel satisfies an evolution equation which governs its dependence on deformations of the boundary surface and generalizes the ordinary (Euclidean) Schrodinger equation. We also derive the classical counterpart of this…

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## References

SHOWING 1-10 OF 22 REFERENCES

Minkowski vacuum in background independent quantum gravity

- Physics
- 2004

We consider a local formalism in quantum field theory, in which no reference is made to infinitely extended spacial surfaces, infinite past or infinite future. This can be obtained in terms of a…

A 'General boundary' formulation for quantum mechanics and quantum gravity

- Physics, Philosophy
- 2003

Schrödinger's cat and the clock: lessons for quantum gravity

- Physics
- 2003

I review basic principles of the quantum mechanical measurement process in view of their implications for a quantum theory of general relativity. It turns out that a clock as an external classical…

Spin Foam Models for Quantum Gravity

- Physics
- 2003

In this topical review, we review the present status of the spin foam formulation of non-perturbative (background-independent) quantum gravity. The topical review is divided into two parts. In the…

Quantum Gravity

- Physics
- 2002

General lectures on quantum gravity. 1 General Questions on Quantum Gravity It is not clear at all what is the problem in quantum gravity (cf. [3] or [8] for general reviews, written in the same…

Introduction to Modern Canonical Quantum General Relativity

- Physics
- 2001

This is an introduction to the by now fifteen years old research field of canonical quantum general relativity, sometimes called "loop quantum gravity". The term "modern" in the title refers to the…

Rept

- Progr. Phys. 64, 1489
- 2001

State sum models for quantum gravity

- Physics
- 2000

This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combinatorial…

Topological quantum field theories

- Physics
- 2000

Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start with…

An Introduction to spin foam models of quantum gravity and BF theory

- Physics
- 1999

In loop quantum gravity we now have a clear picture of the quantum geometry of space, thanks in part to the theory of spin networks. The concept of ‘spin foam’ is intended to serve as a similar…