# Branes and Quantized Fields

## TL;DR

This paper models branes as points in a dynamic infinite-dimensional space, linking classical and quantum descriptions, and introduces a Stueckelberg-like field to address quantum position operator issues.

## Contribution

It develops a novel formalism describing branes as points in a dynamical brane space, unifying classical and quantum perspectives, and introduces Stueckelberg fields to resolve quantum operator challenges.

## Key findings

- Branes can be represented as points in a dynamical infinite-dimensional space.
- Quantization of flat branes yields non-interacting quantum fields.
- A Stueckelberg-like field is introduced to address quantum position operator issues.

## Abstract

It is shown that the Dirac-Nambu-Goto brane can be described as a point particle in an infinite dimensional space with a particular metric. This can be considered as a special case of a general theory in which branes are points in the brane space ${\cal M}$, whose metric is dynamical, just like in general relativity. Such a brane theory, amongst others, includes the flat brane space, whose metric is the infinite dimensional analog of the Minkowski space metric $\eta_{\mu \nu}$. A brane living in the latter space will be called "flat brane"; it is like a bunch of non-interacting point particles. Quantization of the latter system leads to a system of non-interacting quantum fields. Interactions can be included if we consider a non trivial metric in the space of fields. Then the effective classical brane is no longer a flat brane. For a particular choice of the metric in the field space we obtain the Dirac-Nambu-Goto brane. We also show how a Stueckelberg-like quantum field arises within the brane space formalism. With the Stueckelberg fields, we avoid certain well-known intricacies, especially those related to the position operator that is needed in our construction of effective classical branes from the systems of quantum fields.