# Quantum Fields without Wick Rotation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Lorentzian Functional Integral

## 3. Non-Compact Time

#### 3.1. Euclidean, Non-Compact Time

#### 3.2. Lorentzian, Non-Compact Time

#### 3.3. Zeta Function Regularization

## 4. Compact Time

#### 4.1. Euclidean Compact Time

#### 4.2. Lorentzian Compact Time

#### 4.3. Even vs. Odd Dimensions

#### 4.4. The Limit $T\to \infty $.

## 5. Deriving the EA from an RG Equation

#### 5.1. Compact Time with Optimized Regulator

#### 5.2. Compact Time with General Regulator

#### 5.3. Non-Compact Time with General Regulator

## 6. Discussion

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Steepest-descent paths for the integrals ${e}^{i\lambda {x}^{2}}$ with $\lambda >0$ (

**left**) and $\lambda <0$ (

**right**).

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**MDPI and ACS Style**

Baldazzi, A.; Percacci, R.; Skrinjar, V.
Quantum Fields without Wick Rotation. *Symmetry* **2019**, *11*, 373.
https://doi.org/10.3390/sym11030373

**AMA Style**

Baldazzi A, Percacci R, Skrinjar V.
Quantum Fields without Wick Rotation. *Symmetry*. 2019; 11(3):373.
https://doi.org/10.3390/sym11030373

**Chicago/Turabian Style**

Baldazzi, Alessio, Roberto Percacci, and Vedran Skrinjar.
2019. "Quantum Fields without Wick Rotation" *Symmetry* 11, no. 3: 373.
https://doi.org/10.3390/sym11030373