Imaginary free energy and decay rate

In summary, the imaginary part of the free energy in Euclidean quantum field theory, which is defined as the logarithm of the partition function, is connected to the decay rate. The free energy has two components, one with normal parity and one with abnormal parity, where the normal parity component is always real and the abnormal parity component is imaginary. In Minkowskian space, both components are real unless there is phase space for decay, in which case they develop an imaginary part above threshold.
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In euclidean quantum field theory, the imaginary part of the free energy, defined as the logaritm of the partition function, is it connected to the decay rate?
 
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The free energy has two types of components, one without Levi-Civita pseudotensor (normal parity) and another with the epsilon tensor (abnormal parity).
In Euclidean field theory the normal parity component is always real, and the abnormal parity component is imaginary (see e.g.,
L. Alvarez-Gaume. E. Witten, Nucl.Phys. B234 (1984) 269).
In Minkowskian space both components are real if there is no phase space to decay, but develop an imaginary part above threshold (decay, inelastic channels, etc).
 

FAQ: Imaginary free energy and decay rate

What is imaginary free energy?

Imaginary free energy is a theoretical concept used in thermodynamics to describe the energy that is unavailable for work due to the presence of imaginary or complex numbers. It is related to the second law of thermodynamics and is often used in calculations involving chemical reactions.

How does imaginary free energy relate to real free energy?

Real free energy is the measure of the amount of energy available for work in a system. Imaginary free energy is the energy that is not available for work and is often associated with the entropy of a system. The two are related by the equation G = Greal + iGimaginary, where G is the total free energy.

What is decay rate?

Decay rate is a measure of the rate at which a substance or particle decays or loses its energy. It is commonly used in nuclear physics to describe the rate at which radioactive particles decay into more stable forms.

How does decay rate relate to imaginary free energy?

The decay rate of a substance is directly related to its imaginary free energy. As the imaginary free energy of a substance increases, the decay rate also increases. This is because a higher imaginary free energy indicates a greater level of instability in the system, leading to a faster decay rate.

Can imaginary free energy and decay rate be measured?

Yes, both imaginary free energy and decay rate can be measured using various experimental techniques. However, these measurements may be challenging as they often involve complex calculations and require precise and sensitive equipment. Additionally, the values obtained may vary depending on the specific conditions of the system being studied.

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