# Tagged Questions

Fermions are particles with an intrinsic angular momentum (i.e. spin) equal to a "half integer" number of fundamental units: $\frac{(2n+1)}{2} \hbar$ for integer $n$. Fermions are required to be in a quantum state that is globally anti-symmetric, which leads to the Pauli Exclusion Principle barring ...

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### Density depletion for Fermions

In my recent advanced statistical physics class, I read about the density depletion of Fermions, which are "defending" a given volume around them against other Fermions, while the exchange hole ...
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### Can a Fermi gas and a Bose gas be both at the same pressure and temperature?

The title says it all: can a Fermi gas and a Bose gas be both at the same pressure and temperature? It comes from a quiz about statistical mechanics
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Just a quick question - I fail at Googling this topic since I do not remember clearly, in which case (e.g. for what type of particles) is the wave function antisymmetric in terms of spatial rotation $... 2answers 386 views ### Helium Nucleus as boson I am rather perplexed with this fact that though Helium Nucleus is a boson, the particles insides it: protons and neutrons are essentially fermions. How the nucleus which is made by fermions can be a ... 1answer 62 views ### Fermions and Bosons For fermions $$P-\frac{Nk_BT}{V}\geq 0$$ and for bosons, $$P-\frac{Nk_BT}{V}\leq 0$$ What can we understand from these results. 2answers 71 views ### Ambiguity in assigning intrinsic parity We know that, fermions can have intrinsic parity either$\eta_P=+1$or$=-1$. How does one then fix the intrinsic parities ofthe elementary particles, uniquely? Again, the intrinsic parity of a baryon ... 1answer 141 views ### Supersymmetry transformations as coordinate transformations Usually, a supersymmetry transformation is carried out on bosonic and fermionic fields which are functions of the coordinates (or on a superfield which is a function of real and fermionic coordinates).... 1answer 62 views ### Derivation of Fermi level for T>0 I am working through the derivation of the Fermi level$ \mu_0for T>0. However, at one point in the notes I have, it states without any explanation that: $$\int_0^\infty F'(\epsilon) f_{FD}(\... 2answers 70 views ### Why don't we have particles whose wavefunctions are symmetric wrt one exchange operator and anti-symmetric wrt other exchange operator? Consider a system with n identical particles. Let the wavefunction of the system be \psi(r_1,\ldots, r_2). Let P_{a,b} represent the exchange operator which exchanges particle a with particle ... 1answer 72 views ### does electron - positron pair annihilation occur when E is negative? Suppose I release an electron-positron pair from rest at a distance of r. Then the particles attract each other and collide. The total energy E is$$E = 2m_ec^2-\frac{e^2}{4\pi\varepsilon_0r},$$... 2answers 290 views ### Are all fermions massless at high temperatures? According to the standard model, the electroweak symmetry is unbroken at high temperatures, and therefore all gauge bosons are massless then. But since fermions are said to acquire mass by a different ... 2answers 2k views ### Is deuterium a boson or a fermion? I want to know if deuterium is a fermion or boson. Please give me a descriptive answer. I tried the formula that is the combination of protons and electrons which gives odd number but the answer is ... 4answers 2k views ### What is the Difference between a Lepton and a Fermion? As the Title Says: I am Wondering what the Difference between a Lepton and A Fermion is. I know they both have an ½ integer spin number e.g. a electron, an atom with an odd mass number such as Helium-... 1answer 146 views ### How to calculate the speed of electrons in a metal According to the Sommerfeld model, the electrons on the Fermi level has the relation$$ \epsilon_F=\frac{\hbar^2k_F^2}{2m_e}=\frac{1}{2}m_ev_F^2 $$i.e. \hbar k_F=m_ev_F with k_F=(3\pi^2n)^{1/3} ... 2answers 225 views ### Transposition of spinors Suppose we have two 4-components Dirac spinors, that is two non commuting objects, \psi and \chi. We know that: \bar{\psi} \chi= - \chi \bar{\psi} \bar{\psi} = \psi^{+} \gamma_0 +=T* ... 1answer 45 views ### The one-loop contribution to a time ordered product of conserved currents In two dimensions one can define for a Lagrangian describing free Dirac fermions with N associated flavours by$$\mathcal{L}=i\bar{\psi}_i\gamma^\mu \partial_\mu \psi^i $$and associate vector ... 1answer 155 views ### Normal ordering for a two fermion case I am trying to understand how normal ordering works. I am considering a system of two photons, with \hat{f}_i and \hat{f}_i^\dagger being the annihilation and creation operators, respectively. I ... 2answers 238 views ### Why doesn't this multiplication of Grassmann variables give the expected result? Would anyone be able to tell me how srednicki goes from step (44.29) to (44.30)? Here is the paragraph: Now let us introduce the notion of complex Grassmann variables via$$\begin{align} \... 0answers 73 views ### What is really interacting in weak interactions? Only particles with chirality-1$do interact weakly. The corresponding eigenstate in the Dirac basis is$ \Psi_L = \begin{pmatrix}f \\ -f \end{pmatrix} = \begin{pmatrix}u_r {\mathrm{e}}^{-imt} \\ ...
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The generating functional for a free Dirac field is $$Z_0[\eta,\bar{\eta}]=\int D\bar{\psi}D\psi \mathrm{exp}\{i\int [\bar{\psi}(x)S^{-1}\psi(x)+\bar{\eta}(x)\psi(x)+\bar{\psi}(x)\eta(x)]dx\}$$ where ...
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### Are the left-chiral and right-chiral yukawa couplings equal?

I guess another way to ask this is: Does the "physical electron" spend EQUAL time being a left-chiral and right-chiral fermion, on average? Clarification: The electron switches between (-1/2 T3, -1Y) ...
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### Geometric interpretation of Grassmann variable

Grassmann variables were introduced to make path-integral formalism easier to handle fermionic (anti-commutating) fields. Mathematically they represent the exterior algebra of forms (or exterior ...