Unruh Effect (1+1)D: Understanding Equation 5.68

In summary, the Unruh Effect (1+1)D is a phenomenon in quantum field theory that describes the creation of particles by an accelerating observer in two-dimensional spacetime. Equation 5.68, derived by physicist Bill Unruh, relates the energy density and temperature of the quantum field to the acceleration of an observer in (1+1)D spacetime. This effect differs from the Unruh Effect in higher dimensions, as it is a simplified version that is easier to calculate and understand. Equation 5.68 is significant because it allows for a quantitative understanding of the relationship between acceleration, temperature, and energy density in (1+1)D spacetime. The Unruh Effect (1+1)
  • #1
thatboi
121
18
Hi all,
I am trying to work through the Unruh Effect for the (1+1)-dimensional massive scalar field case and came across the paper I attached. However, I am trying to derive equation 5.68, but am greatly struggling with the prefactor on the left hand side. When comparing the left hand side to (5.64), it is clear that there is an extra factor of \frac{1}{\sqrt{2\pi}} that seems to appear out of nowhere. Can someone provide assistance? Thank you.
 

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  • #2
thatboi said:
came across the paper I attached.
Can you give a link to where you obtained it?
 
  • #3
Perhaps (5.42) could be the key.
 

Related to Unruh Effect (1+1)D: Understanding Equation 5.68

1. What is the Unruh Effect (1+1)D?

The Unruh Effect (1+1)D, also known as the Unruh-DeWitt detector model, is a theoretical concept in quantum field theory that describes the phenomenon of particle creation and detection in a uniformly accelerating frame of reference. It is a simplified version of the full Unruh Effect, which applies to a higher-dimensional spacetime.

2. What is Equation 5.68 in the Unruh Effect (1+1)D?

Equation 5.68 is a mathematical formula that represents the probability of a particle being detected by an Unruh-DeWitt detector in a uniformly accelerating frame of reference. It takes into account factors such as the acceleration of the observer and the energy of the particle being detected.

3. How does the Unruh Effect (1+1)D relate to the Hawking radiation?

The Unruh Effect (1+1)D and Hawking radiation are both phenomena that involve the creation and detection of particles in a gravitational field. However, the Unruh Effect applies to uniformly accelerating frames of reference, while Hawking radiation applies to black holes.

4. Can the Unruh Effect (1+1)D be observed in real life?

Currently, there is no experimental evidence for the Unruh Effect (1+1)D. However, some scientists believe that it may be possible to observe it in the future by using advanced technology to create a uniformly accelerating frame of reference.

5. What are the implications of the Unruh Effect (1+1)D?

The Unruh Effect (1+1)D has important implications for our understanding of quantum field theory and the nature of particles. It also has potential implications for the study of black holes and the behavior of particles in extreme gravitational fields.

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