pqTensorfeld

PqTensorfeld is a mathematical concept that extends the idea of a tensor field to include p-adic numbers. In traditional tensor analysis, tensor fields are functions that assign a tensor to each point in a space, typically using real or complex numbers. PqTensorfeld, on the other hand, uses p-adic numbers, which are part of the p-adic number system. This system is characterized by a different metric, where the distance between two numbers is determined by their highest power of a prime p that divides their difference.

The p-adic metric is ultrametric, meaning that the triangle inequality is strengthened to the ultrametric inequality. This leads to a topology where open balls are both open and closed, and the space is totally disconnected. These properties make p-adic numbers and their tensor fields useful in certain areas of mathematics and physics, such as number theory and quantum field theory.

In a pqTensorfeld, the tensor at each point is a p-adic tensor, which is defined similarly to a real tensor but with p-adic components. The operations on these tensors, such as addition, multiplication, and contraction, are adapted to the p-adic number system. This includes the use of p-adic absolute values and norms.

PqTensorfelds have been studied in the context of p-adic quantum mechanics and p-adic string theory, where they provide a different perspective on quantum phenomena and string dynamics. They also appear in the study of p-adic differential geometry, where they are used to define p-adic manifolds and their geometric properties.