What is Gamma: Definition and 711 Discussions

Gamma (uppercase Γ, lowercase γ; Greek: γάμμα gámma) is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. In Ancient Greek, the letter gamma represented a voiced velar stop /ɡ/. In Modern Greek, this letter represents either a voiced velar fricative or a voiced palatal fricative.
In the International Phonetic Alphabet and other modern Latin-alphabet based phonetic notations, it represents the voiced velar fricative.

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  1. R

    Understanding Traceless Proof for Gamma Matrices

    I'm reading through some lecture notes and there is a proof that the gamma matrices are traceless that I've never seen before (I've seen the "identity 0" on wikipedia proof) and I can't work out some of the steps: \begin{align*} 2\eta_{\mu\nu}Tr(\gamma_\lambda) &=...
  2. H

    Deriving the Expression for Total Energy: Understanding E = gamma mc^2

    Hi, How exactly does one derive ##E = \gamma mc^2##? Is this an expression for "total energy" contained in an object? The velocity of an object differs between frames of reference right? So doesn't that mean that E differs between frames as well? If it varies between frames can it even...
  3. H

    How Does the Skin Effect Differ from Gamma Ray Penetration in Conductors?

    Skin Effect: . where = resistivity of the conductor = angular frequency of current = 2π × frequency = relative magnetic permeability of the conductor = the permeability of free space ------------------------------ From Wiki According to Skin Effect, the higher the frequency, the less...
  4. A

    MHB Integration using Beta and Gamma Functions

    Interestingly, I seem to have an integral I have posted before, but I want to take a different approach to it. $\int_{0}^{1} \frac{\ln(1+x)}{1+x^2} \,dx$ The beta function states, $B(x,y) = \int_{0}^{1} {t}^{x-1}({1-t}^{y-1}) \,dx$ So, I was just thinking if there a possible way to compute...
  5. C

    Contour integral involving gamma function

    Homework Statement Evaluate the integral by closing a contour in the complex plane $$\int_{-\infty}^{\infty} dx e^{iax^2/2}$$ Homework Equations Residue theoremThe Attempt at a Solution My initial choice of contour was a semicircle of radius R and a line segment from -R to R. In the limit R to...
  6. Spinnor

    1 dimensional crystal at rest, a nucleus emits gamma ray of energy E,

    Say we have a one dimensional chain of N mass points separated by springs of spring constant k. This system can be quantized? Let the quantized system above be at rest and let one of the end mass points emit a photon of energy E along the crystal axis. Will we get physics similar to he...
  7. marcus

    Gamma ray bursts (GRB) and distribution of life

    Gammaray bursts (GRB) may affect the prevalence of life in various different regions of the galaxy. http://arxiv.org/abs/1409.2506 On the role of GRBs on life extinction in the Universe Tsvi Piran, Raul Jimenez (Submitted on 8 Sep 2014) As a copious source of gamma-rays, a nearby Galactic...
  8. S

    Question about Lorentz Invariance and Gamma Matrices

    This is a pretty basic question, but I haven't seen it dealt with in the texts that I have used. In the proof where it is shown that the product of a spinor and its Dirac conjugate is Lorentz invariant, it is assumed that the gamma matrix \gamma^0 is invariant under a Lorentz transformation. I...
  9. ChrisVer

    Schwarz's Metric Gamma: Inertial Coordinates & Time Dilation

    Can the above logic be applied to Schw. Metric as well? Suppose I have an object moving with a radial velocity v=const, then can I do the same to derive the Schwarchild time dilation as in the Minkowski? dr = v ~ dt ds^{2} = [K - \frac{v^2}{K} ] dt^2 So \gamma ^{-1} = \sqrt{K} [1 -...
  10. B

    Pulling a rope on a wall, finding gamma

    Homework Statement Determine coordinate direction angle γ of the resultant force acting at B. Homework Equations Cos\gamma = F\underline{}z/F The Attempt at a Solution The first part was to find magnitude of F\underline{}b. The next part was finding the other coordinate...
  11. H

    The factorial of a rational number, the gamma function not used

    My first question is: is this formula (at the bottom) a known formula? In this subject i haven't explained how i build up the formula. So far i think it is equal to the gamma function of Euler with \Gamma\left(\frac{m_1}{m_2}+1\right)= \frac{m_1}{m_2}\ ! with m_1 , m_2 \in...
  12. B

    Simplifying expression with gamma matrix and slashes

    I am trying to simplify the expression \not p \gamma^\mu \not p. I believe the answer should be - \frac{1}{2} \gamma^\mu p^2, but I am not sure. Tom
  13. mesa

    Question about the Borwein fast algorithm for certain values of Gamma

    I am reading through Borwein's paper, "Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind" and have a question. If we look at his algorithm's we see they are of this general form...
  14. mesa

    Looking for Borwein's/Zucker's fast algorithm for the gamma function.

    I have heard that the Borwein/Zucker algorithm for computing certain values of the gamma function is pretty awesome, but finding it online is proving elusive... Does anyone know the algorithm?
  15. T

    Gamma rays induced fission of silicon

    Hey everyone I'm new here and this is my first thread, although i have great interest in chemistry and physics my knowledge of these fields is very basic( I'm graduated in economics) so don't be surprised if i ask something that may look silly. so here are my firsts questions. -Is it...
  16. Greg Bernhardt

    Can the Gamma Function Simplify Complex Integrals?

    Definition/Summary The gamma function denoted by \Gamma (n) is defined by \Gamma (n) = \int_{0}^{\infty} x^{n-1} e^{-x} dx is convergent for real and complex argument except for 0, -1, -2, ...-k Equations Useful identities: \Gamma(n+1)=n! \Gamma (x+1) = x\Gamma(x)...
  17. pellman

    Is this section of the wikipedia page for gamma matrices wrong?

    http://en.wikipedia.org/wiki/Gamma_matrices#Normalization See the image below. Which of us is right: me or Wikipedia?
  18. R

    Co60, Gamma Spec, Different Counts in Peaks

    Hi Board, In the Spectrum of Co60 http://upload.wikimedia.org/wikipedia/commons/thumb/2/24/Co60_Spectrum.JPG/776px-Co60_Spectrum.JPG i see the two peaks of the 4-2-0 Cascade. Looking at a table of Nuclides http://atom.kaeri.re.kr/cgi-bin/decay?Co-60%20B- i found that the peaks...
  19. K

    Gamma Ray Burst datasets that consist of distance modulus & redshift

    Hi guys I am looking for a dataset to use in my thesis. I am working on UNION 2.1 sample of supernovea Ia data. That dataset consist of redshift and distance modulus with uncertainty (sigma) for 590 supernovea. Do you guys know where can i find similar dataset for GRBs?
  20. M

    Any good books on gamma functions

    Are there any good textbooks for gamma functions? Explaining them? Because I need to evaluate stuff like ∫e^x^3 dx or ∫sin(x^2) dx
  21. D

    Can Crystals Absorb X-rays and Gamma Rays to Emit RF for Movement Tracking?

    Hi guys, Could someone refer me to sources which explain and give examples for crystals which absorb xray / gamma ray and emit RF ? Meaning that if I radiate a crystal with xray I get RF so I can theoretically track its movement in the enclosed are. Thanks a lot!
  22. J

    How to Calculate the Correct Fraction of Monatomic Molecules in a Gas Mixture?

    Homework Statement An experiment you're designing needs a gas with γ = 1.49. You recall from your physics class that no individual gas has this value, but it occurs to you that you could produce a gas with γ = 1.49 by mixing together a monatomic gas and a diatomic gas. What fraction of the...
  23. P

    How to simplify this summation to an incomplete gamma function

    Could someone please explain why the following sum simplifies to the following? = As far as I can see, this sum does not correlate to the formula for incomplete gamma function as a sum. I'd appreciate any help as the incomplete gamma function is somewhat beyond the scope of my current...
  24. T

    Gamma distribution from sample mean of Exponential distribution

    Homework Statement Let X1, X2,...,Xn be a random sample from the exponential distribution with mean θ and \overline{X} = \sum^{n}_{i = 1}X_i Show that \overline{X} ~ Gamma(n, \frac{n}{θ}) Homework Equations θ = \frac{1}{λ} MGF Exponential Distribution = \frac{λ}{λ - t} MGF Gamma...
  25. C

    Pion Decay into Gamma rays angle

    So i have a question regarding a homework question I'm working on which suggest a neutral pion traveling with velocity v decays into two gamma rays of equal theta to the normal and they of course have velocity c. It then asks to prove that v= cos theta Which kind of confuses me. I mean if...
  26. Saitama

    MHB Solving a definite integral without using gamma function

    Problem: Evaluate: $$\int_0^{\infty} t^{-1/4}e^{-t}\,dt$$ Attempt: I recognised this one as $\Gamma(3/4)$. I found a few formulas on Wolfram Mathworld website which helps to evaluate this but I am wondering if I can solve the definite integral from elementary methods (like by parts). Any help...
  27. A

    Lorentz, waves, Einstein and bodies: transformations +/- gamma

    I am using a wikipedia page, Derivation of the Lorentz transformations and a lot of historical papers. To follow through I came up with my own transformations that do not contain the gamma factor: ##x^{'}=x-\beta ct## ##t^{'}=t-\beta \frac{x}{c}## When applying them to a waveform...
  28. A

    Gamma plus or minus gamma-beta, two different outcomes?

    In Wikipedia it reads that γ(1+β) = \sqrt{\frac{1+β}{1-β}}, however, if I did my homework correctly I get γ(1+β) = \sqrt{\frac{1+β^{2}}{1-β^{2}}}. Digging more deeply into why Wikipedia is listing it as such I found that it is based on the hyperbolic angles:γ=coshΘ. But it leads to definitions...
  29. E

    Gamma Function and the Euler-Mascheroni Constant

    I was taking a break from studying from my real analysis, electrodynamics, and nuclear physics exams this week, and, being a math-phile, I decided to play around with the gamma-function for some reason. Anyway, I used the common product expansion of the multiplicative inverse, and I arrived at a...
  30. mesa

    Need sources to search for gamma function infinite series identities.

    I have a hard time believing we only have the limited number of series I have seen so far especially considering how much broader mathematics is than I had thought just a short while ago. Where should I search to find more infinite series summations for the gamma function? For example which...
  31. mesa

    Do we have a general solution infinite series for the gamma function?

    Does anyone know if we currently have an infinite series summation general solution for the gamma function such as, $$\frac{1}{\Gamma(k)}=\sum_{n=0}^{\infty} f(n,k)$$ or, $${\Gamma(k)}=\sum_{n=0}^{\infty} f(n,k)$$?
  32. T

    Gamma spectroscopy- Fine Gain Coarse Gain factors

    I'm currently doing a spectroscopy lab where you use a scintillator and Cs-137 to obtain a Cs-137 spectrum. I calibrated this spectrum using the known gamma energy for Cs-137 at 662 Kev at the photo peak. I am now trying to use this calibration for a Co-60 spectrum. The problem is that when I...
  33. U

    Relationship between the Chi_squared and Gamma Distributions ?

    Hi, It has been a long time since I have worked with pdfs so perhaps someone can help. According to Wikipedia (http://en.wikipedia.org/w/index.php?title=Chi-squared_distribution#Additivity) the pdf of the addition of n independend Chi_squared distributed R.V.s is also Chi_squared distributed...
  34. H

    Representing the Gamma Function

    I'm not sure if this is a "general" math question but I do think it is an interesting one. The Gamma Function, \Gamma(t), has many interesting definitions. It can take on the form of an integral to an infinite product. There is one particular definition, however, that I am trying to...
  35. A

    Puzzle with moment generating function for gamma function

    I am given that The kth moment of an exponential random variable with mean mu is E[Y^k] = k!*mu^k for nonnegative integer k. I found m^2 (0) = (-a)(-a-1)(-beta)^2. The answer I found is however mu^2+a*beta^2 which is different from the k! From the given formula. Could someone help me figure it...
  36. |Glitch|

    Gamma Ray Burst GRB 130427A: The Brightest Explosion in the Universe

    I recently read the following article: It was not very long, and it did not contain much information. However, after a little searching I discovered the article was referring to GRB 130427A. The key features of this GRB are its strength at 94 GeV, and its duration at "better part of a...
  37. A

    Is chirality dependent on the representation of the gamma matrices?

    Hi, In QFT we define the projection operators: \begin{equation} P_{\pm} = \frac{1}{2} ( 1 \pm \gamma^5) \end{equation} and define the left- and right-handed parts of the Dirac spinor as: \begin{align} \psi_R & = P_+ \psi \\ \psi_L & = P_- \psi \end{align} I was wondering if the left- and...
  38. T

    Exploring Spin in Different Dimensions: 2+1 and Beyond

    Dear PhysicsForum, We have just treated the Dirac equation and its lagrangian during our QFT course, but we have only gone in depth in 3+1 dimensions. My question is about what happens to spin in 2+1 dimensions. In 3+1 dimensions we have to use 4 by 4 gamma matrices, but in 2+1 dimensions we...
  39. C

    What is Channel Number? (In gamma spectroscopy)

    Really quick question. In a graph like this: http://en.wikipedia.org/wiki/File:Cs137_Spectrum.PNG Source What does the Channel Number represent? Also, just to make sure, am I right in saying the count rate is \frac{\delta m}{\delta t} ? where m is the cumulative number of scintillations and...
  40. R

    Gamma Func Help: Solve F(alpha+1)=alpha*F(alpha)

    http://img202.imageshack.us/img202/3224/620u.jpg In A for this question F(alpha+1)=alpha*F(alpha) and I'm curious as to how the RHS of this still has the gamma function in it?
  41. Y

    Expected Value of Inverse Gamma Distribution

    Homework Statement I have that X is distributed with Gamma(a,b) and that Y = \frac{1}{X}. I found the pdf of Y to be \frac{1}{\Gamma(a)b^a} \left(\frac{1}{y}\right)^{a+1} e^{-1/yb} for y > 0. I need to use this to find the expected value. Homework Equations The gamma function is...
  42. C

    Nuclear Physics: Recoil in gamma decay

    Homework Statement Question wants you to a) find the difference between Egamma and the excitation energy of the nucleus due to the fact that the nucleus recoils. (using approximation that Egamma is small relative to nucleus mass. other parts are simple if I can get a)Homework Equations...
  43. C

    Proving the Gamma Matrix Identity in QFT: Is There a Mistake in My Attempt?

    Homework Statement Prove that \gamma^{a}\gamma^{b}\gamma^{c}\gamma^{d}\gamma^{e}\gamma_{a} = 2\left(\gamma^{e}\gamma^{b}\gamma^{c}\gamma^{d}+\gamma^{d}\gamma^{c} \gamma^{b}\gamma^{e}\right) Each of the \gamma^{i}s are as used in the Dirac equation. Homework Equations...
  44. C

    Integrating a x^k ln(x) Function with Gamma Function

    Homework Statement "Show that - \int^1_0 x^k\ln{x}\,dx = \frac{1}{(k+1)^2} ; k > -1. Hint: rewrite as a gamma function. Homework Equations Well, I know that \Gamma \left( x \right) = \int\limits_0^\infty {t^{x - 1} e^{ - t} dt}. The Attempt at a Solution I've tried various substitutions...
  45. jim mcnamara

    Gamma ray bursts (GRB's) and the Ordovician Mass Extinction

    99% of all marine fossil generating species on Earth that ever existed have gone extinct. There are periods in the fossil record that show massive extinction rates. For example, the K-T (now the K-Pg) boundary marks the extinction of dinosaurs in the fossil record along with marine animals, at...
  46. A

    Shaping time on my amplifier alters the gamma energy registered?

    Hi, My understanding of shaping time on amplifiers is that its the amount of time the capacitor has to collect charge. I would say that the longer the time the better energy resolution you would have due to that all the charge created from the photon is collected. However, if the time is long...
  47. A

    Gamma spectroscopy regarding Cs-137

    Hi, I was doing a measurement on a Cs-137 source, strong enough so that my detector registers a sum peak. I can't get my head around A, the peak at ~80 keV.. I get B (backscatter peak), C(compton edge) and D total abs.peak. I tried with a weaker Cs-137 and I saw the 35keV (Ba) but no...
  48. B

    Radio waves to gamma particle question

    Hi all, so iv'e been looking around and can't find an answer to a question i have. I have read articles on wikipedia and understand the "basics", but i still cannot fully visualize the concept. Question: Do all frequencies on the em spectrum emit the same particles? i know that visible "light"...
  49. T

    Approximating the gamma function near x=-3

    I've just started self studying James Nearing's "Mathematical Tools for Physicists" (available at http://www.physics.miami.edu/~nearing/mathmethods/mathematical_methods-three.pdf), and I'm having trouble with problem 1.16 about the gamma function, defined for positive x as \Gamma(x)=...
  50. M

    Gamma Spectroscopy for Estimating Radiological Risk in Rocks

    Am currently doing an undergraduate project work on 'estimation of radiological risk pose by U-238, th-232 and K-40 in rock samples' . The instrument I'll use are NaI(TI) crystal for scintilation were the gamma rays from the source(my rock samples) interact with the crystal through photoelectric...
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