# 2D Systems and 4D Minkowski Space: Exploring Path Integrals

• DMESONS
In summary, the combination of special relativity and quantum mechanics in a single framework only applies to 4D systems in Minkowski space. Recent published work has explored the idea of reducing 4D systems to 2D systems, using two-dimensional field theories such as the thirring model and two-dimensional conformal field theory. More information on this can be found in the book "Unification and Supersymmetry" by Rabindra N. Mohapatra.
DMESONS
The combination of special relativity and quantum mechanics in a single framework makes our understanding of such systems to be true only in 4D, Minkowski space...I have noticed that recent published work concerning 2D systems and I am not sure about this reduction of 4D to only 2D, does it mean evaluating path integrals (e.g. correlation functions) by considering (1,1)=(time,space) in order to simplify the calucualtions?

Could you please give a reference regarding the publications you are talking about?

Polyrhythmic said:
Could you please give a reference regarding the publications you are talking about?

Many refs. but for example;

http://arxiv.org/abs/1208.6568

## 1. What is the difference between 2D systems and 4D Minkowski space?

2D systems refer to physical systems that exist in two dimensions, typically represented by a plane. On the other hand, 4D Minkowski space is a mathematical concept that extends the three dimensions of space and one dimension of time into a four-dimensional spacetime. While 2D systems are limited to two spatial dimensions, 4D Minkowski space includes all four dimensions and allows for a deeper understanding of the universe.

## 2. What are path integrals and how are they used to study 2D systems and 4D Minkowski space?

Path integrals are mathematical tools used to calculate the probability of a particle moving from one point to another in a given amount of time. In the context of 2D systems and 4D Minkowski space, path integrals are used to study the behavior and interactions of particles in these dimensions. They allow for the prediction and analysis of various physical phenomena, such as quantum mechanics and general relativity.

## 3. Can 2D systems and 4D Minkowski space coexist in the same universe?

Yes, 2D systems and 4D Minkowski space can coexist in the same universe. While we live in a 3D world with one dimension of time, there are theories and mathematical models that suggest the existence of additional dimensions. These dimensions may not be directly observable, but they can still play a role in the behavior and interactions of particles in our universe.

## 4. How does studying path integrals in 4D Minkowski space impact our understanding of the universe?

Studying path integrals in 4D Minkowski space allows for a more comprehensive understanding of the universe. It helps us to better understand the behavior of particles and their interactions in the four dimensions of spacetime. This can lead to advancements in fields such as quantum mechanics, cosmology, and particle physics, ultimately deepening our understanding of the fundamental laws that govern our universe.

## 5. What are some real-world applications of studying 2D systems and 4D Minkowski space?

Studying 2D systems and 4D Minkowski space has various real-world applications, including the development of new technologies and improved understanding of physical phenomena. For example, path integrals have been used in the development of quantum computers and in predicting the behavior of subatomic particles. Additionally, understanding the concepts of 4D Minkowski space has aided in the development of theories such as the Big Bang theory and the theory of relativity.

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