Scalar Definition and 773 Threads

Consider a cube of edge a. There is a point charge q at each corner. Find \phi at the center of the face for which x=a. The answer to the problem is \0.707*(q/\epsilon_0*a) I have to use the the scalar potential equation, but I have been stuck on this problem for a while. I know that I have to...

Prove: If V is a finite dimensional vector space and T is in L(V), then there exists a finite list of scalars ao,a1,a2,...,an, not all 0 such that aoX + a1T x + a2T^2 x... + anT^n x = theata for all x in V my hint for the question is: the powers of T are defined as T^0 = I, T^1 = 1...

I am working with a complex scalar field written in terms of two independent real scalar fields and trying to derive the commutator relations. So, \phi = \frac{1}{\sqrt{2}} \left(\phi_1 + i \phi_2) where \phi_1 and \phi_2 are real. When deriving...

(Or if you prefer: Why are things defined this way?) I noticed that, in my book's definition, scalar multiplication (SM) on vector spaces lacks two familiar things: commutativity and inverses. The multiplicative inverse concept doesn't seem to apply to SM. Can it? I can't imagine how it could...

Hi all, I am having some problems understanding the steps in a paper. I've looked in books and asked other grad students but they have all not been of too much help and I am still stuck. I have a massive scalar field mass \mu interacting with two delta function potentials with...

There´s an assertion that the electric field depends only on Vector potential in radiation region. But I couldn´t see clearly why the contribution of scalar potential could be comparatively ignored. Could anyone give me some explanations? Thanks!

what do they mean when they say "neutrino scalar waves travel back and forwards in time"?and why does it happen for neutrino?

Should your answer include the constant of integration? I think it should but my book's answers don't, so I dunno. Example, <2xy^3, 3y^2x^2> answer is x^2y^3, but should I include the + C? (and yes I went through and made sure h(y) was in fact a constant

According to the definition, an operator T that commutes with all components of the angular momentum operator is a scalar, or rank zero, operator. What is the mathematical definition to that statement? How can I prove that the four dimensional Laplacian is a scalar operator? Regards, :biggrin:

How? I know that a scalar quantity only comprises of magnitude while a vector consist of both magnitude and direction.. But is there no definite formula to determine whether or not a quantity is a scalar or a vector.. or is there a list of scalars and vectors to show all quantities...

Greetings, I stumbled across two question that I have no idea on how to answer them. 1) The interaction term in a scalar field theory is -\frac{\lambda}{4!} \phi^4 Why should lambda be positive? (they say look at the energy of the ground state...) 2) Write down the Feynman rules for...

Like I said I need physicists and meteorologists Could scalar waves be cause of: Artificially cause volcanoes' eruptions(because scalar waves can easily penetrate thru Earth's core,some people think that was the cause ST. Helen's volcano erupted-true or false) To artificially cause...

Hi, I have a question about a statement I've seen in many a Quantum Field Theory book (e.g. Zee). They say that the general form of the Lagrangian density for a scalar field, once two conditions are imposed: (1) Lorentz invariance, and (2) At most two time derivatives, is: L =...

This one: a)Let V be a vector space and let x be a vector in V. i)Show that b0=0 for each scalar b. ii)Show that if bx=0, then either b=0 or x=0

Hi there, I have a problem that I could really do with a little help on. I have a spin 1/2 particle in which the dirac eqtn reads: ( i {d} - \gamma V(x) - m ) \Phi = 0 (I am new to latex - the d is SLASHED and the gamma is GAMMA5 ) In a potential V(x,t) = 0 for...

Consider the two vectors M =(a,b) = ai+bj and N = (c,d) = ci +dj, where a =4, b =4, c = -1, and d = 1. a and c represent the x-displacment and b and d represent the y-displacment in a Cartesian xy co-ordinate system. Note: i and j represent unit vectors(i.e. vectors of length l)in the x and y...

How do you find a unit vector normal to the surface of scalar field \phi(x,y,z)=x^2y+3xyz+5yz^2? Should you apply the \nabla operator to it?

Hi everybody, I have a small question. I know that we have defined multiplication of a number and a vector ,for example b*A (capital letters =vectors, everything else=real numbers). We have also defined that b*(c*A)=(b*c)*A. From these two rules is a*b*c*d*...*k*Z defined (= product of n...

Hi what is the definition and meaning (geometric) of a vector valued and scalar valued function? I read the definition in the textbook but I didn't quite get it. Thank you.

I was reading about Weyl Transformations in Polchinski's book and I have a little doubt: Is it correct to say that under a Weyl transformation the scalars are invariant, i.e., that a weyl transformation preserves the scalar product?

Scalar equations such as y=2x+3 actually generate POINTS which are collinear. A vector equation, as the name implies, generates VECTORS, and these vectors are definitely NOT COLLINEAR. How then can we say that an equation such as r = (2,1,3) + t(1,2,4) is the "equation of a line"...

can someone explain this to me please?

I'm wondering if physics ever uses a differential equation of the form of a curl of a gradient of a scalar function. Or is this too trivial? Thanks.